Oswaal JEE (Main) Mock Test, 15 Sample Question Papers, Physics, Chemistry, Mathematics Book (For 2021 Exam) [1 ed.] 9789354230004

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• PHYSICS •CHEMISTRY •MATHEMATICS

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1ST EDITION, YEAR 2021

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2011

HYDERABAD

PREFACE ‘Arise! Awake! and Stop Not till the Goal is reached’ Swami Vivekananda



We are living in a world where science and technology is everywhere, engineers have completely changed the world. For every student who chooses to go in the field of engineering, IIT JEE (Main) is the first step in the journey of their engineering career. However, simply clearing JEE isn’t adequate. High competition makes it imperative to score as high as possible, to guarantee that you get admission in the best engineering institution. Taking note of the disruption caused to students’ learning because of the ongoing pandemic, the NTA has taken various measure to help the students. As per its latest circular released on 16th Dec 2020, JEE (Main) Exam will be conducted four times in 2021, in the months of February, March, April and May. This time the candidates will be required to attempt only 75 questions out of 90 or 25 out of 30 questions in each section. Unlike 2020, when subject wise there were 5 numeric value questions, this year i.e., in 2021, subject wise there will be 10 numeric value questions, where candidates can choose any five questions to answer. Oswaal Mock Test 15 Sample Question Papers is designed based on these recent changes which makes them extremely relevant for JEE (Main) 2021 Exam. Oswaal Books is continuously working in the direction of spreading knowledge since the past 40 years. Here we have designed a Oswaal Mock Test 15 Sample Question Papers for candidates appearing for JEE (Main) 2021 Exam.

Benefits of solving these Mock Test Series are:



• Oswaal Mock Test 15 Sample Question Papers Designed after a thorough research & include all typologies of Questions specified by the NTA.



• JEE (Main) 2019 & 2020 Solved Papers



• Get on top of the test paper pattern with Subjective Analysis



• Mind Maps of related subjects; Physics, Chemistry and Mathematics



• Oswaal Mnemonics to boost memory and confidence



• Easy to Scan QR Codes for online content

This book aims to make the aspiring candidates’ exam-ready, boost their confidence and help them achieve the desired results. With the moto of ‘Learning made Simple’, Oswaal Books is constantly striving to make learning simple & feasible for students across the country.

With Best Wishes! Team Oswaal (5)

(6)

CONTENTS g

Latest Syllabus for Academic Year 2021

g

JEE (Main) Trend Analysis – 2019 and 2020

19 - 21

g

10 Tips to Crack JEE (Main) Exam

22 - 23

g

Mind Maps & Mnemonics – Physics, Chemistry and Mathematics

1 - 116

8 - 18

 JEE (Main) – 2020 Solved Paper

117 - 141

 JEE (Main) – 2019 Solved Paper

142 - 171

 Mock Test Paper-1

172 - 180

 Mock Test Paper-2

181 - 190

 Mock Test Paper-3

191 - 200

 Mock Test Paper-4

201 - 209

 Mock Test Paper-5

210 - 219

 Mock Test Paper-6

220 - 228

 Mock Test Paper-7

229 - 238

 Mock Test Paper-8

239 - 248

 Mock Test Paper-9

249 - 258

 Mock Test Paper-10

259 - 268

 Mock Test Paper-11

269 - 279

 Mock Test Paper-12

280 - 289

 Mock Test Paper-13

290 - 299

 Mock Test Paper-14

300 - 309

 Mock Test Paper-15

310 - 319 qq

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JEE (Main) Latest Syllabus for Academic Year (2021) PHYSICS The syllabus contains two sections - A and B. Section - A pertains to the Theory Part having 80% weightage, while Section - B contains Practical Component (Experimental Skills) having 20% weightage.

motion; moment of a force, torque, angular momentum, conservation of angular momentum and its applications; moment of inertia, radius of gyration. Values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications. Rigid

SECTION - A

body rotation, equations of rotational motion.

UNIT 1: PHYSICS AND MEASUREMENT

UNIT 6: GRAVITATION

Physics, technology and society. S I units. Fundamental and derived units. Least count, accuracy and precision of measuring instruments. Errors in measurement. Dimensions of Physical quantities, dimensional analysis and its applications.

The universal law of gravitation. Acceleration

UNIT 2: KINEMATICS

UNIT 7: PROPERTIES OF SOLIDS AND LIQUIDS

Frame of reference. Motion in a straight line: Position time graph, speed and velocity. Uniform and non-uniform motion, average speed and instantaneous velocity Uniformly accelerated motion, velocity-time. position-time graphs, relations for uniformly accelerated motion. Scalars and Vectors. Vector addition and Subtraction, Zero Vector, Scalar and Vector products. Unit vector, Resolution of a Vector. Relative Velocity, Motion in a plane, Projectile Motion, Uniform Circular Motion. UNIT 3: LAWS OF MOTION

due to gravity and its variation with attitude and depth. Kepler’s laws of planetary motion. Gravitational potential energy; gravitational potential. Escape velocity, Orbital velocity of a satellite, Geo-stationary satellities.

Elastic

behaviour,

Stress-strain

relationship,

Hooke’s Law, Young’s modulus, bulk modulus, modulus of rigidity, Pressure due to a fluid column; Pascal’s law and its applications, Viscosity, Stokes’ Law, Reynolds number, Bernoulli’s principle and its applications. Surface energy and surface tension, angle of contact, application of surface tension- drops , bubbles and capillary rise. Heat, temperature, thermal expansion; specific Heat capacity, calorimetry; change of state, latent heat, Heat transferconduction, convection and radiation, Newton’s law of

Force and Inertia, Newton’s First law of motion; Momentum, Newton’s Second Law of motion; Impulse; Newton’s Third Law of motion. Law of conservation of linear momentum and its applications. Equilibrium of concurrent forces.

cooling.

Static and Kinetic friction, laws of friction, rolling friction.

internal energy, First law of thermodynamics, Second law

Dynamics of uniform circular motion; Centripetal force and its applications.

UNIT 8: THERMODYNAMICS Thermal

equilibrium,

zeroth

law

of

thermodynamics, concept of temperature. Heat, work and of thermodynamics: reversible and irreversible processes, Carnot engine and its efficiency.

UNIT 4: WORK, ENERGY AND POWER

UNIT 9: KINETIC THEORY OF GASES

Work done by a constant force and a variable force; kinetic and potential energies, workenergy theorem, power.

Equation of state of a perfect gas, work done on

Potential energy of a spring, conservation of mechanical energy, conservative and nonconservative forces; Elastic and inelastic collisions in one and two dimensions.

rms speed of gas molecules; Degrees of freedom, Law

UNIT 5: ROTATIONAL MOTION

UNIT 10: OSCILLATIONS AND WAVES

Centre of mass of a two-particle system, Centre

Periodic motion- period, frequency, displacement

of mass of a rigid body: Basic concepts of rotational

as a function of time. Periodic functions, Simple harmonic

compressing a gas. kinetic theory of gases- assumptions, concept of pressure, kinetic energy and temperature: of equipartition of energy, applications to specific heat capacities of gases; Mean free path, Avogadro’s number.

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...CONTD. motion (S.H.M) and its equation; phase; oscillations of

UNIT 13: MAGNETIC EFFECTS OF CURRENT AND

a spring- restoring force and force constant; energy in

MAGNETISM

S.H.M, - kinetic and potential energies; Simple pendulumderivation of expression for its time period; Free, forced and damped oscillations, resonance. Wave motion, Longitudinal and transverse waves, speed of a wave,Displacement relation for a progressive wave. Principle of superposition of waves, reflection of waves, Standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect in sound.

charges;

Conservation

carrying circular loop. Ampere’s law and its applications to infinitely long current carrying straight wire and solenoid. Force on a moving charge in uniform magnetic and electric fields. Cyclotron. Force on a current- carrying conductor in a uniform magnetic field. Force between two parallel current carrying conductors- definition of ampere. Torque experienced by

UNIT 11: ELECTROSTATICS Electric

Biot- Savart law and its application to current

a current loop in uniform magnetic field; Moving coil of

charge,

galvanometer, its current sensitivity and conversion to

Coulomb’s law- forces between two point charges, forces

ammeter and voltmeter.

between multiple charges; superposition principle and

Current loop as a magnetic dipole and its magnetic dipole

continuous charge distribution.

moment, Bar magnet as an equivalent solenoid, magnetic

Electric field: Electric field due to a point charge. Electric

field lines, Earth’s magnetic field and magnetic elements.

field lines, Electric dipole, Electric field due to a dipole,

Para-dia-and ferro-magnetic substances.

Torque on a dipole in a uniform electric field.

Magnetic susceptibility and permeability, Hysteresis,

Electric flux, Gauss’s law and its applications to find field

Electromagnets and permanent magnets.

due to infinitely long uniformly charged straight wire,

UNIT 14: ELECTROMAGNETIC INDUCTION AND

uniformly charged infinite plane sheet and uniformly charged thin spherical shell. Electric potential and its calculation for a point charge, electric dipole and system of charges; Equipotential surfaces, Electrical potential energy of a system of two point charges in an electrostatic field. Conductors and insulators, Dielectrics and electric polarization, capacitor, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor

ALTERNATING CURRENTS Electromagnetic

induction;

Faraday’s

law,

induced emf and current; Lenz’s Law, Eddy currents, Self and mutual inductance. Alternating currents, peak and rms value of alternating current/ voltage; reactance and impedance; LCR series circuit, resonance; Quality factor power in AC circuits, wattless current AC generator and transformer.

with and without dielectric medium between the plates,

UNIT 15: ELECTROMAGNETIC WAVES

Energy stored in a capacitor.

Electromagnetic waves and their characteristics.

UNIT 12: CURRENT ELECTRICITY

Transverse nature of electromagnetic waves.

Electric current, Drift velocity, Ohm’s law. Electrical resistance, Resistances of different materials, V-I characteristics of Ohmic and nonohmic conductors, Electrical energy and power. Electrical resistivity, Colour code for resistors; Series and parallel combinations of resistors; Temperature dependence of resistance.

Electromagnatic spectrum (radio waves, microwaves, infrared,

visible,

ultraviolet,

Xrays,

gamma

rays).

Applications of e.m. waves. UNIT 16: OPTICS Reflection and refration of light at plane and spherical surfaces, mirror formula, Total internal reflaction

Electric Cell and its Internal resistance, potential

and its applications, Deviation and Dispersion of light by

difference and emf of a cell, combination of cells in series

a prism, Lens Formula, Magnification, Power of a Lens,

and in parallel. Kirchhoff ’s laws and their applications.

Combination of thin lenses in contact, Microscope and

Wheatstone bridge, Metre bridge, Potentiometer- principle

Astronomical Telescope (reflecting and refracting) and

and its applications.

their magnifying powers.

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...CONTD. Wave optics: wavefront and Huygen’s principle, Laws of reflection and refraction using Huygen’s principle. Interference,

Young’s

double

slit

experiment

and

SECTION - B UNIT 21: EXPERIMENTAL SKILLS

expression for fringe width, coherent sources and



sustained interference of light, Diffraction due to a

of the experiments and activities:

single slit, width of central maximum. Resolving power

1.

Vernier callipers- its use to measure internal and

of microscopes and astronomical telescopes, Polarisation,



external diameter and depth of a vessel.

plane polarized light; Brewster’s law, uses of plane polarized light and Polaroids. UNIT

17:

DUAL

NATURE

Familiarity with the basic approach and observations

2. Screw gauge- its use to determine thickness/

OF

MATTER

AND

diameter of thin sheet/wire.

3. Simple Pendulum- dissipation of energy by

RADIATION



plotting a graph between square of amplitude

Dual nature of radiation, Photoelectric effect,



and time.

Hertz and Lenard’s observations; Einstein’s photoelectric

4.

Metre Scale- mass of a given object by principle

equation; particle nature of light, Matter waves-wave



of moments.

nature of particle, de Broglie relation, Davisson- Germer

5.

Young’s modulus of elasticity of the material of a

experiment.



metallic wire.

UNIT 18: ATOMS AND NUCLEI

6. Surface tension of water by capillary rise and

Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum. Composition and size of nucleus, atomic masses, isotopes, isobars: isotones. Radioactivity-alpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass- energy relation, mass defect; biding energy per nucleon and its variation with mass

7.

Co-efficient of Viscosity of a given viscous liquid



by measuring terminal velocity of a given



spherical body.

8. Plotting a cooling curve for the relationship

between the temperature of a hot body and

time.

UNIT 19: ELECTRONIC DEVICES semiconductor

effect of detergents.

9. Speed of sound in air at room temperature

number, nuclear fission and fusion.

Semiconductors,



diode:

1-V

characteristics in forward and reverse bias; diode as a rectifier; I-V characteristics of LED, photodiode, solar cell and zener diode: zener diode as a voltage regulator. Junction transistor, transistor action. characteristics of a transistor; transistor as an amplifier (common emitter

using a resonance tube.

10. Specific heat capacity of a given (i) solid and (ii)

liquid by method of mixtures.

11. Resistivity of the material of a given wire using

metre bridge.

12. Resistance of a given wire using Ohm’s law.

13. Potentiometer :

configuration) and oscillator. Logic gates (OR, AND, NOT,

(i) Comparison of emf of two primary cells.

NAND and NOR). Transistor as a switch.

(ii) Determination of internal resistance of a cell.

UNIT 20: COMMUNICATION SYSTEMS Propagation of electromagnetic waves in the atmosphere; Sky and space wave propagation, Need for modulation, Amplitude and Frequency Modulation

14. Resistance and figure of merit of a galvanometer

by half deflection method.

15. Focal length of:

Bandwidth of signals, Bandwidth of Transmission

(i) Convex mirror

medium, Basic Elements of a Communication System

(ii) Concave mirror, and

(Block Diagram only).

(iii) Convex lens using parallax method.

( 10 )

...CONTD. 16. Plot of angle of deviation vs angle of incidence for a triangular prism.

items.

22. Using multimeter to:

17. Refractive index of a glass slab using a travelling microscope.

(i) Identify base of a transistor.

18. Characteristic curves of a p-n junction diode in forward and reverse bias.

transistor.

(ii) Distinguish between npn and pnp type

19. Characteristic curves of a zener diode and finding reverse break down voltage.

(iii) See the unidirectional flow of current in

20. Characteristic curves of a transistor and finding current gain and voltage gain.

(iv) Check the correctness or otherwise of a



21. Identification of Diode, LED, Transistor, IC, Resistor, Capacitor from mixed collection of such



case of a diode and an LED.

given

electronic

component

(diode,

transistor or IC). 

For Subjective Appendix Physics

CHEMISTRY Gaseous State:

SECTION - A

Measurable properties of gases; Gas laws- Boyle’s law, Charle’s law, Graham’s law of diffusion, Avogadro’s law, Dalton’s law of partial pressure;

PHYSICAL CHEMISTRY Unit 1 : Some Basic Concepts in Chemistry



Matter and its nature, Dalton’s atomic theory; Concept of atom, molecule, element and compound; Physical quantities and their measurements in Chemistry, precision and accuracy, significant figures, S.I. units, dimensional analysis; Laws of chemical combination; Atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae; Chemical equations and stoichiometry.





Classification of matter into solid, liquid and gaseous states.

Liquid State:

Properties of liquids- vapour pressure, viscosity and surface tension and effect of temperature on them (qualitative treatment only).

Unit 2 : States Of Matter

Concept of Absolute scale of temperature; Ideal gas equation; Kinetic theory of gases (only postulates); Concept of average, root mean square and most probable velocities; Real gases, deviation from Ideal behaviour, compressibility factor and van der Waals equaation.

Solid State:

Classification of solids: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea); Bragg’s Law and its

( 11 )

...CONTD. applications; Unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids, calculations involving unit cell parameters, imperfection in solids; Electrical and magnetic properties.

Unit 3 : Atomic Structure



Thomson and Rutherford atomic models and their limitations; Nature of electromagnetic radiation, photoelectric effect; Spectrum of hydrogen atom, Bohr model of hydrogen atomits postulates, derivation of the relations for energy of the electron and radii of the different orbits, limitations of Bohr’s model; Dual nature of matter, de- Broglie’s relationship, Heisenberg uncertainty principle. Elementary ideas of quantum mechanics, quantum mechanical model of atom, its important features. Concept of atomic orbitals as one electron wave functions; Variation of Ψ and Ψ2 with r for 1s and 2s orbitals; various quantum numbers (principal, angular momentum and magnetic quantum numbers) and their significance; shapes of s, p and d-orbitals, electron spin and spin quantum number; Rules for filling electrons in orbitalsaufbau principle, Pauli’s exclusion principle and Hund’s rule, electronic configuration of elements, extra stability of half- filled and completely filled



Unit 5 : Chemical Thermodynamics



Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, state functions, types of processes





First law of thermodynamics: Concept of work, heat internal energy and enthalpy, heat capacity, molar heat capacity; Hess’s law of constant heat summation; Enthalpies of bond dissociation, combustion, formation, atomization, sublimation, phase transition, hydration, ionization and solution.





Second law of thermodynamics; Spontaneity of processes; ∆S of the universe and ∆G of the system as criteria for spontancity, ∆G0 (Standard Gibbs energy change) and equilibrium constant.

Unit 6 : Solutions

orbitals.

Unit 4 : Chemical Bonding and Molecular Structure



Kossel - Lewis approach to chemical bond formation, concept of ionic and covalent bonds.

Ionic Bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds; calculation of lattice enthalpy.

Covalent Bonding: Concept of electronegativity, Fajan’s rule, dipole moment; Valence Shell Electron Pair Repulsion (VSEPR) theory and shapes of simple molecules.

Quantum mechanical approach to covalent Bonding: Valence bond theory - Its important features, concept of hybridization involving s, p and d orbitals; Resonance. Molecular Orbital Theory: Its important features, LCAOs, types of molecular orbitals (bonding, antibonding), sigma and pi-bonds, molecular orbital electronic configurations of homonuclear diatomic molecules, concept of bond order, bond length and bond energy.

Elementary idea of metallic bonding. Hydrogen bonding and its applications.



Different methods for expressing concentration of solution- molality, molarity, mole fraction, percentage (by volume and mass both), vapour pressure of solutions and Raoult’s Law- Ideal and non-ideal solutions, vapour pressure composition, plots for ideal and non-ideal solutions; Colligative properties of dilute solutions - relative lowering of vapour pressure, depression of freezing point, elevation of boiling and osmotic pressure; Determination of molecular mass using colligative properties; Abnormal value of molar mass, van’t Hoff factor and its significance.

Unit 7 : Equilibrium Meaning of equilibrium, concept of dynamic equilibrium. Equilibria involving physical processes: Solidliquid, liquid- gas and solid - gas equilibria, Henry’s law, general characteries of equilibrium involving physical processes. Equilibria involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, significance of ∆G and ∆G0 in chemical equilibria, factors affecting equilibrium concentration, pressure, temperature, effect of catalyst; Le Chatelier’s principle.

( 12 )

...CONTD.

Ionic equilibrium : Weak and strong electrolytes, ionization of electrolytes, various concepts of acids and bases (Arrhenius , Bronsted - Lowry and Lewis) and their ionization, acid- base equilibria (including multistage ionization) and ionization constants, ionization of water, pH scale, common ion effect, hydrolysis of salts and pH of their solutions, solubility of sparingly soluble salts and solubility products, buffer solutions.

Colloidal state- distinction among true solutions, colloids and suspensions, classification of colloids - lyophilic, lyophobic; multimolecular, macromolecular and associated colloids (micelles), preparation and properties of colloids - Tyndall effect, Brownian movement, electrophoresis, dialysis, coagulation and flocculation; Emulsions and their characteristics.

SECTION - B

Unit 8 : Redox Reactions And Electro Chemistry



Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions.



Electrolytic and metallic conduction, conductance in electrolytic solutions, molar conductivities and their variation with concentraton: Kohlrausch’s law and its application.



Electrochemical cells- Electrolytic and Galvanic cells, different types of electrodes, electrodes potentials including standard electrode potential, half- cell and cell reactions, emf of a Galvanic cell and its measurement; Nernst equation and its applications; Relationship between cell potential and Gibbs’ energy change; Dry cell and lead accumulator; Fuel cells.

INORGANIC CHEMISTRY Unit 11 : Classification Of Elements And Periodicity In Properties

Unit 12 : General Principles And Processes Of Isolation Of Metals



Unit 9 : Chemical Kinetics



Rate of a chemical reaction, factors affecting the rate of reactions; concentration, temperature, pressure and catalyst; elementary and complex reactions, order and molecularity of reactions, rate law, rate constant and its units, differential and integral forms of zero and first order reactions, their characteristics and half lives, effect of temperature on rate of reactions- Arrhenius theory, activation energy and its calculation, collision theory of bimolecular gaseous reactions (no derivation).

Unit 10 : Surface Chemistry



Adsorption- Physisorption and chemisorption and their characteristics, factors affecting adsorption of gases on solids- Freundlich and Langmuir adsorption isotherms, adsorption from solutions.

Catalysis- Homogeneous and heterogeneous, activity and selectivity of solid catalysts, enzyme catalysis and its mechanism.

Modern periodic law and present form of the periodic table, s, p, d and f block elements, periodic trends in properties of elements atomic and ionic radii, ionization enthalpy, electron gain enthalpy, valence, oxidation states and chemical reactivity.

Modes of occurrence of elements in nature, minerals, ores; Steps involved in the extraction of metals- concentration, reduction(chemical and electrolytic methods) and refining with special reference to the extraction of Al, Cu, Zn and Fe; Thermodynamic and electrochemical principles involved in the extraction of metals.

Unit 13 : Hydrogen



Position of hydrogen in periodic table, isotopes, preparation, properties and uses of hydrogen; Physical and chemical properties of water and heavy water; Structure, preparation, reactions and uses of hydrogen peroxide; Classification of hydrides- ionic, covalent and interstitial; Hydrogen as a fuel.

Unit 14 : S-Block Elements (Alkali And Alkaline earth Metals)



Group - 1 and 2 Elements



General introduction, electronic configuration and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships.



Preparation and properties of some important compounds- sodium carbonate and sodium

( 13 )

...CONTD. hydroxide and sodium hydrogen carbonate; Industrial uses of lime, limestone, Plaster of Paris and cement; Biological significance of Na, K, Mg and Ca,

occurrence and characteristics, general trends in properties of the first row transition elements - physical properties, ionization enthalpy, oxidation states, atomic radii, colour, catalytic behaviour, magnetic properties, complex formation, interstitial compounds, alloy formation; Preparation, properties and uses of K2, Cr2, O2 and KMnO4

Unit 15 : P-Block Elements

Group - 13 to Group 18 Elements General Introduction : Electronic configuration and general trends in physical and chemical properties of elements across the periods and down the groups; unique behaviour of the first element in each group.

Groupwise study of the p- block elements

Inner Transition Elements

Actinoids - Electronic configuration and oxidation states.

Group - 13

Preparation, properties and uses of boron and aluminium; Structure, properties and uses of borax, boric acid, diborane, boron trifluoride, aluminium chloride and alums.

Unit 17 : Co-Ordination Compounds



Group - 14 Tendency for catenation; Structure, properties and uses of Allotropes and oxides of carbon, silicon tetrachloride, silicates, zeolites and silicones. Group - 15 Properties and uses of nitrogen and phosphorus; Allotrophic forms of phosphorus; Preparation, properties, structure and uses of ammonia, nitric acid, phosphine and phosphorus halides, (PCI3, PCI5); Structures of oxides and oxoacids of nitrogen and phosphorus. Group - 16 Preparation, properties, structures and uses of ozone; Allotropic forms of sulphur; Preparation, Properties, structures and uses of sulphuric acid (including its industrial preparation); Structures of oxoacids of sulphur. Group - 17 Preparation, properties and uses of hydrochloric acidl; Trends in the acidic nature of hydrogen halides; Structures of Interhalogen compounds and oxides and oxoacids of halogens. Group - 18 Occurrence and uses of noble gases; Structure of fluorides and oxides of xenon.

Unit 16 : d-and f - Block Elements Transition Elements

Lanthanoids - Electronic configuration, oxidation states and lanthanoid contraction.

General introduction, electronic configuration,

Introduction

to co-ordination compounds, Werner’s theory; ligands, co-ordination number, denticity, chelation; IUPAC nomenclature of mononuclear co-ordination compounds, isomerism; Bonding-Valence bond approach and basic ideas of Crystal field theory, colour and magnetic properties; Importance of coordination compounds (in qualitative analysis, extraction of metals and in biological systems).

Unit 18 : Environmental Chemistry



Environmental Pollution- Atmospheric, water and soil.

Atmospheric Stratospheric.

Pollution- Tropospheric and

Tropospheric pollutants- Gaseous pollutants: Oxides of carbon, nitrogen and sulphur, hydrocarbons; their sources, harmful effects and prevention; Green house effect and Global warming: Acid rain; Particulate pollutants- Smoke, dust, smog, fumes, mist; their sources, harmful effects and prevention. Stratospheric pollution- Formation and breakdown of ozone, depletion of ozone layer- its mechanism and effects. Water pollution- Major pollutants such as, pathogens, organic wastes and chemical pollutants; their harmful effects and prevention. Soil pollution- Major pollutants such as: Pesticides (insecticides, herbicides and fungicides), their harmful effects and prevention.

( 14 )

Strategies to control enviromental pollution.

...CONTD. Alkynes- Acidic character; Addition of hydrogen, halogens, water and hydrogen halides; Polymerization.

SECTION- C ORGANIC CHEMISTRY Unit 19 : Purification And Characterisation Of Organic Compounds

Purification- Crystallization, sublimation, distillation, differential extraction and chromatography- principles and their applications.

Qualitative analysis- Detection of nitrogen, sulphur, phosphorus and halogens.

Aromatic hydrocarbonsNomenclature, benzene- structure and aromaticity; Mechanism of electrophilic substitution; halogenation, nitration, Friedel- Craft’s alkylation and acylation, directive influence of functional group in monosubstituted benzene.

Unit 22 : Organic Compounds Containing Halogens

Quantitative analysis (basic principles only)Estimation of carbon, hydrogen, nitrogen, halogens, sulphur, phosphorus.





General methods of preparation, properties and reactions; Nature of C-X bond; Mechanisms of substitution reactions.







Uses; Environmental effects of chloroform, iodoform freons and DDT.

Calculations of empirical formulae and molecular formulae; Numerical problems in organic quantitative analysis.

Unit 20 : Some Basic Principles Of Organic Chemistry



Tetravalency of carbon; Shapes of simple molecules- hybridization (s and p); Classification of organic compounds based on functional groups: and those containing halogens, oxygen, nitrogen and sulphur; Homologous series; Isomerism structural and stereoisomerism.

Nomenclature (Trivial and IUPAC) Covalent bond fission - Homolytic and heterolytic; free radicals, carbocations and carbanions; stability of carbocations and free radicals, electrophiles and nucleophiles. Electronic displacement in a covalent bond - Inductive effect, electromeric effect, resonance and hyperconjugation. Common types of organic reactions- Substitution, addition, elimination and rearrangement.

Unit 21 : Hydrocarbons



Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties and reactions.

Alkanes - Conformations; Sawhorse and Newman projections (of ethane); Mechanism of halogenation of alkanes. Alkenes - Geometrical isomerism; Mechanism of electrophilic addition: addition of hydrogen, halogens, water, hydrogen halides ( Markownikoff ’s and peroxide effects); Ozonolysis and polymerization.

Unit 23 : Organic Compounds Containing Oxygen



General methods of preparation, properties reactions and uses.

ALCOHOLS, PHENOLS AND ETHERS

Alcohols : Identification of primary, secondary and tertiary alcohols; mechanism of dehydration.

Phenols : Acidic nature, electrophilic substitution reactions; halogenation, nitration and sulphonation, Reimer- Tiemann reaction. Ethers : Structure Aldehyde and Ketones: Nature of carbonyl group; Nucleophilic addition to >C=O group, relative reactivities of aldehydes and ketones; Important reaction such as - Nucleophilic addition reactions (addition of HCN, NH3 and its derivatives), Grignard reagent; oxidation; reduction (Wolff Kishner and Clemmensen); activity of α-hydrogen, aldol condensation, Cannizzaro reaction, Haloform reaction; Chemical tests to distinguish between aldehydes and Ketones. Carboxylic Acids Acidic strength and factors affecting it.

Unit 24 : Organic Compounds Containing Nitrogen



General methods of preparation, properties, reactions and uses.

Amines : Nomenclature, classification, structure, basic character and identification of primary, secondary and tertiary amines and their basic character.

( 15 )

...CONTD. Diazonium Salts : Importance in synthetic organic chemistry

Cleansing agents - Soaps and detergents, cleans-

Unit 25 : Polymers

Unit 28 : Principles Related To Practical Chemistry

General introduction and classification of polymers, general methods of polymerizationaddition and condensation, copolymerization.

Natural and synthetic rubber and vulcanization: some important polymers with emphasis on their monomers and uses- polythene, nylon, polyester and bakelite.

Unit 26 : Biomolecules General introduction and importance of biomolecules. Carbohydrates - Classification: Aldoses and ketoses; monosaccharides (glucose and fructose) and constituent monosaccharides of oligosaccharides (sucrose, lactose and maltose). Proteins - Elementary Idea of -amino acids, peptide bond, polypeptides: Proteins: primary, secondary, tertiary and quaternary of proteins, eanzymes.

ing action.

 Detection of extra elements (N, S, halogens) in organic compounds; Detection of the following functional groups: hydroxyl (alcoholic and phenolic). carbonyl (aldehyde and ketone). carboxyl and amino groups in organic compounds.

 Chemistry involved in the preparation of the following:



Inoganic compounds: Mohr’s salt, potash alum.



Organic compounds: Acetanilide, p-nitroacetanilide, aniline yellow, iodoform.

 Chemistry involved in the titrimetric excercisesAcids bases and the use of indicators, oxalic- acid vs KMnO4, Mohr’s salt vs KMnO4.

 Chemical principles involved in the qualitative salt analysis: Cations- Pb2+, Cu2+, Ai3+, Fe3+, Zn2+, Ni2+, Ca2+, Ba2+, Mg2+, NH +4

Vitamins - Classification and functions.



Anions- CO32 − S2- SO2 − NO3− NO − Cl–, Br–, I– 4 2 ,

Nucleic acids - Chemical constitution of DNA



(Insoluble salts excluded)



 Chemical principles involved in the following experiments:



1. Enthalpy of solutions of CuSO4



2. Enthalpy of neutralization of strong acid and strong base.



3. Preparation of lyophilic and lyophobic sols.



4. Kinetic study of reaction of iodide ion with hydrogen peroxide at room temperature.





and RNA.

Biological functions of nucleic acids. Unit 27 : Chemistry In Everyday Life



Chemical in medicines - Analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamins - their meaning and common examples.

Chemical in food - Preservatives, artificial sweetening agents- common examples.

,

,

qq



For Subjective Appendix Chemistry

( 16 )

...CONTD. MATHEMATICS UNIT 1 : SETS, RELATIONS AND FUNCTIONS

UNIT 7 : SEQUENCES AND SERIES





Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Type of relations, equivalence relations, functions; one-one, into and onto functions, composition of functions.

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special series: S n, S n2, Sn3. Arithmetic-Geometric progression.

UNIT 2 : COMPLEX NUMBERS AND QUADRATIC EQUATIONS

UNIT 8 : LIMIT, CONTINUITY AND DIFFERENTIABILITY





Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.

sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two. Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals.

UNIT 3 : MATRICES AND DETERMINANTS

Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

UNIT 4 : PERMUTATIONS AND COMBINATIONS

Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.



Principle of Mathematical Induction and its simple applications.

UNIT 6 : BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS

UNIT 9 : INTEGRAL CALCULUS

Integral as an anti - derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities.



Evaluation of simple integrals of the type

∫x

UNIT 5 : MATHEMATICAL INDUCTION

Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the



Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications.

( 17 )

2

dx dx dx dx dx , , , , , ± a 2 ∫ x 2 ± a 2 ∫ a 2 − x 2 ∫ a 2 − x 2 ∫ ax 2 + bx + c

∫

dx ax 2 + bx + c

∫

,∫

( px + q )dx ( px + q )dx , , ax 2 + bx + c ∫ ax 2 + bx + c

a 2 ± x 2 dx,

∫

x 2 − a 2 dx,

Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

...CONTD. UNIT 10 : DIFFERENTIAL EQUATIONS

UNIT 12 : THREE DIMENSIONAL GEOMETRY





Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type : dy + p( x) y = q( x) dx

UNIT 13 : VECTOR ALGEBRA

UNIT 11 : CO-ORDINATE GEOMETRY

Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines.

Cartesian system of rectangular co-ordinates 10 in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.



Straight lines



Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines.

Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product.

UNIT 14 : STATISTICS AND PROBABILITY

Measures of Dispersion : Calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.



Probability : Probability of an event, addition and multiplication theorems of probability. Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.



Circles, conic sections

UNIT 15 : TRIGONOMETRY



Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of a the tangent. Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.



Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances.

UNIT 16 : MATHEMATICAL REASONING

Statements, logical operations and, or, implies, implied by, if and only if. Understanding of tautology, contradiction, converse and contrapositive.

qq

For Subjective Appendix Mathematics

( 18 )

TREND ANALYSIS JEE (MAIN) 2019 & 2020 PHYSICS Total Papers Chap. No.

Chapter Name

8

8

6

10

Jan 2019

Apr 2019

Jan 2020

Sep 2020

Phase - 1

Phase - 2

Phase - 1

Phase - 2

1

Physics and Measurement

8

7

5

10

2

Kinematics

14

11

6

11

3

Laws of Motion

5

4

3

6

4

Work, Energy and Power

6

10

9

10

5

Rotational Motion

18

19

16

21

6

Gravitation

6

7

3

11

7

Properties of Solids and Liquids

6

13

7

9

8

Thermodynamics

18

13

11

16

9

Kinetic Theory of Gases

6

10

6

12

10

Oscillations and Waves

20

19

7

15

11

Electrostatics

23

20

12

21

12

Current Electricity

20

16

8

12

13

Magnetic Effects of Current

23

19

9

22

14

Electromagnetic Induction and Alternating Currents

9

11

9

14

15

Electromagnetic Waves

7

6

5

8

16

Optics

20

19

14

21

17

Dual Nature of Matter and Radiation

7

9

6

10

18

Atoms and Nuclei

9

11

6

11

19

Electronic Devices

8

9

8

8

20

Communication Systems

7

7

0

2

240

240

150

250

Total Questions



( 19 )

TREND ANALYSIS JEE (MAIN) 2019 & 2020 CHEMISTRY Total Papers Chap. No.

Chapter Name

8

8

6

10

Jan 2019

Apr 2019

Jan 2020

Sep 2020

Phase - 1

Phase - 2

Phase - 1

Phase - 2

1

Some Basic Concepts in Chemistry

4

4

5

11

2

States of Matter

10

8

4

8

3

Atomic Structure

9

10

4

9

4

Chemical Bonding & Molecular Structure

4

6

4

8

5

Chemical Thermodynamics

12

9

6

7

6

Solutions

11

10

6

7

7

Equilibrium

10

10

7

13

8

Redox Reactions and Electrochemistry

9

10

8

14

9

Chemical Kinetics and Surface Chemistry

15

15

10

21

10

Classification of Elements and Periodicity in Properties

5

4

6

11

11

General Principles and Processes of Isolation of Metals

8

9

4

7

12

Hydrogen, s & p - Block Elements

21

20

15

23

13

d & f - Blocks Elements and Coordination Compounds

19

25

19

23

14

Environmental Chemistry

13

9

2

6

15

Purification, Basic Principles and Characteristics of Organic Compounds

11

18

8

13

16

Hydrocarbons and their Halogen Derivatives

8

16

12

12

17

Organic Compound Containing Oxygen

31

19

10

25

18

Organic Compound Containing Nitrogen

12

14

5

7

19

Polymers and Biomolecules

12

16

7

13

20

Analytical Chemistry and Chemistry in Everyday life

16

8

8

12

240

240

150

250

Total Questions



( 20 )

TREND ANALYSIS JEE (MAIN) 2019 & 2020 MATHEMATICS Total Papers Chap. No.

Chapter Name

8

8

6

10

Jan 2019

Apr 2019

Jan 2020

Sep 2020

Phase - 1

Phase - 2 Phase - 1 Phase - 2

1

Sets, Relations and Functions

8

11

5

10

2

Complex Numbers and Quadratic Equations

15

14

12

19

3

Matrices and Determinants

17

15

13

20

4

Permutation and Combination

8

8

6

9

5

Mathematical Induction

1

0

0

0

6

Binomial Theorem and Its Simple Application

11

10

5

11

7

Sequence and Series

13

17

11

20

8

Limit Continuity and Differentiability

31

31

26

37

9

Integrals Calculus

25

26

15

21

10

Differential Equations

7

8

7

11

11

Coordinate Geometry

39

37

15

30

12

Three Dimensional Geometry

16

18

5

12

13

Vector Algebra

8

7

7

9

14

Statistics And Probability

17

16

12

21

15

Trigonometry

17

14

5

10

16

Mathematical Reasoning

7

8

6

10

240

240

150

250

Total Questions



( 21 )

...CONTD. 7. Revise Whenever You Get Time Make sure you revise as much as possible. The revision will help you in keeping the concepts fresh in your mind until the day of the final examinations. You may refer to a few good Question Banks, Sample Papers and your self-made notes for this purpose.

8. Keep A Track on Time While you are solving papers, make sure you keep a track on time i.e., how much time does it take to solve one sections and the type of questions which take minimum and maximum time.

9. Exam Day Strategy First & foremost, try to be in time at the exam centre, it will help you keep yourself calm. Scoring good marks is all about identifying the questions which you should be attempting first and the ones which are to be solved in the second round. Always try to attempt those questions first which seems familiar, less time consuming and easy.

10. Keep Yourself Motivated & Healthy Don’t be Anxious, keep yourself Calm! Taking care of your thought process and keeping it positive is the first and the best course of action that one is required to take. This time is very important for you, so is everything you are eating or thinking. Eat healthy and easy to digest food and take proper sleep. Always remember that to achieve good scores you will need consistent efforts and calm mind. Trust on your honest efforts, if in case at any point of time you feel stressed, don’t be hesitant in taking help from counsellors or family members. Your focus should only be on clearing the JEE exam and to give your best shot.



All the Best !!

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PHYSICS MIND MAPS & MNEMONICS

2

Oswaal JEE (Main) Mock Test 15 Sample Question Papers



x = v0t + at

(ii)

A

B

Kinematics Part-1

t

vavg



Rate of change of position of an object w.r.t time in given direction .It in vector quantity Av er ag e



x t

Total displacement  Total time taken

y cit lo e V

In opposite direction, it will be sum and in same direction, it will be difference for the same frame of reference

(ii)

   vAB  vn  vB  A  vBn  vB  vA

a n-1) 2

a

Rate of change of velocity w.r.t. time,  v Types

orm

  x vinst  lim t  0 t   dx dt





Av e

v 1t 1  v2 t2  .....  vn tn t 1  t 2  .....  t n

When object traversed different speeds in different time of intervals.

S1 + S2 + S3+....Sn t1 + t2 + t3+....tn

When object traversed different distances with different time.

Distance traversed/time taken . Scalar quantity

The shotest distance traversed by any object in called displacement  It in a vector quantity. 

Total length of the path traversed by any object is called its distance  It is scalar quantity. 

When the magnitude or the direction of velocity changes w.r.t. time. o ti o n

n

ment Displace

e tanc Dis

Non - uni form m

if Un

ti o Mo

Equal distances are traversed in equal amount of time.

  v dv a inst lim  t  0 t dt

eed Sp e g ra

(i)

(iv) xnth = v0+

2 2 (iii) v = v0 + 2ax

v = v+ at 0

(i)

Free Fall

ns of quatio tic e a n motion nem cceleratio Ki a ly rm i fo n u

Earth’s gravity (g= 9.8m/s2) on neglecting air resistance. It is a case of motion with uniform acceleration. e.g Apple falling from a tree.

An object falling because of

Total time interval  v  t

Total change in velocity

Acceleration

aavg 

Ve locity



Mind Maps

3



2 Horizontal range,R = u sin2θ g

Total time of flight,Tf = 2u sinθ g Maximum height,Hmax = u2sin2θ 2g

Vectors having common starting point.

If, A = – B



Vectors having same magnitude but opposite direction   eg. A is a negative of B

Vectors having same direction and magnitude

gnitu It has magnitude as one or unity  A ^ A =  A

Equ

Pla ne

tile jec n o tio Pr mo

Mo tio ni na

Kinematics Part-2

x=(ucosθ)t;

y=(u sinθ) t - 1 gt2 2

Motion of an object that is in flight after being thrown or projected.

r

Vec to

→ P

Addition of Vectors

tile ation of path of projec

g y=x tanθ– 2 2 x2 2u cos

→ P

Law of Parallelogram Law of Triangle → → → R=P+Q → → → → R R Q Q

at any instant po ax = 0,ay = g C o m

→ → |V & AB|=| VBA|

→ → VAB = –VBA

→→ → → V BA = VB –VA

→ → → V AB =VA –VB

ac=v2/r = r2 = 4π2 r2

A body in a circular motion acted upon by an acceleration directed towards centre of the circular motion.

Angular velocity ,ω= θ/t Angular acceleration,d=∆ω/∆t eg- merry go around.

When an object follows a circular path at a constant speed , the motion of the object is called uniform circular motion.

→ a = axi + ayj; ax=dvx/dt & ay= dvy/dt → |a|=√ax2+ay2

→ v =vx i + vy j , → magnitude|v | = √vx2+vy2

→ i + y^ j Position vector , r = x^ → Displacement vector ,  r =  x^ j i +y^

→ → λ A=λA

u= ucosθ,u= u sinθ x y

Motion of Body under two dimensional frame.

→→ → → A–B=A+(–B)

ne

It has zero magnitude and orbitary direction

ele r a ti o n

f acc

Centripeta l

n ts o

4 Oswaal JEE (Main) Mock Test 15 Sample Question Papers Acce lera tio n

Moti on of a

ca ro n

o n est

st

d roa el v e al

Opposes impending relative motion FS = µsR

Kinetic Fric tion

A push or pull which changes or tends to change state of rest or of uniform motion of a body.

or µR < µk < µs

Oppose actual rolling motion FR < Fk 2s>1s

y

2px

Z

2pz

x y x Size.4p>3p>2p

y

Z

Z

2py

x dxy

y

dx2–y2

y

x

x

dyz

z y

dz2

Z

dxz

z

x

d Orbitals – ‘’Clover leaf ’’ distribution. – Two angular nodes.

x

Dual nature i.e. wave like and particle like of the electromagnetic radiation. • Experimental results regarding atomic spectra. • Wave nature of electromagnetic radiation. It was given by James Maxwell. Frequency (ν): Number of waves that pass a given point in one second. Unit – Hertz (Hz), Velocity of light = Frequency × Wavelength Wave number (–ν): Number of wavelengths per unit length. Unit – m-1 • Particle nature of electromagnetic radiation: Planck's quantum theory: E= hν Planck's constant (h) = 6.626 × 10–34 Js p Orbitals: Each p Orbital consists of two sections called lobes on either side of plane passing through the nucleus.

Lower the value of (n+l) for an orbital, lower is its energy.

Positive space

Electron

Postulates: • Positive charge and most of the mass of atoms was densely concentrated in extremely small region i.e. nucleus. • Nucleus is surrounded by electrons that move around the nucleus with high speed in circular path called orbits. • Electrons and nucleus are held together by electrostatic forces of attraction. Drawbacks: • It cannot explain the stability of an atom. • It does not say anything about the electronic structure of atoms.

Atom possesses a spherical shape in which the positive charge is uniformly distributed.

By James Chadwick Charge on neutron = 0 Mass of neutron= 1.675 × 10–27 Kg

By Ernest Rutherford Charge on proton = +1.6022 × 10–19C Mass of Proton= 1.672 × 10–27 Kg

By J.J.Thomson Charge to mass ratio of electron = 1.758820 × 1011 C kg-1 Charge electron = 1.6022 × 10–19C Mass of electron = 9.1094 × 10–31Kg

: (Watermelon M odel of Atom odel) so n M Thom Rutherford's Nuclear Model of A tom

y over Disc

Atoms of different elements with different atomic number but same mass number. 40 (40 20Ca and 18Ar)

Atoms of same element having same atomic number but different mass number. (Isotopes of hydrogen: 1 Protium 1 H, Deuterium 21 D and

rs

Number of protons (Z) + number of neutrons (n)

ba Iso

Number of protons in nucleus of an atom or Number of electrons in a neutral atom

Bohr's Model for Hyd

• Emission Spectra : Spectrum of radiation emitted by a substance that has absorbed energy. • Absorption Spectra : It is like photographic negative of an emission spectra. • Line / Atomic Spectra : Emission spectra which do not show a continuous spread of wavelength from red to violet, rather they emit light only at specific wavelength with dark space between them. – = 109677 ( 1 1 ) cm–1 where v n12 n22 n1=1,2………….n2=n1+1, n1+2……… Series n1 n2 Spectral Region Ultraviolet Lyman 2,3......... 1 Balmer Visible 2 3,4......... Paschen 3 Infrared 4,5......... Brackett 4 Infrared 5,6......... Pfund 5 6,7......... Infrared

Mind Maps

39

(i) Bond Length : Equilibrium distance between the nuclei of two bonded atoms in molecule. (ii) Bond Angle : Angle between the orbitals containing bonding electron pairs around central atom in a molecule complex ion. (iii) Bond Enthalpy : Amount of energy required to break one mole of bonds of particular type between two atoms. (iv) Bond Order : Number of bonds between the two atoms of a molecule. (v) Resonance Structures : A set of two or more Lewis structures that collectively describe the electronic bonding a single polyatomic species. (vi) Dipole Moment : Product of the magnitude of the charge and distance between centres of positive and negative charge. µ= Q x r

Postulates : • Shape of molecule depends upon the number of valence shell electron pairs around central atom. • Pairs of electrons in the valence shell repel one another. • These pairs of electrons tend to occupy such positions in space that minimize repulsion. • The valence shell is taken as a sphere with electron pairs localising on spherical surface at maximum distance from one another. • A multiple bond is treated as if it is a single electron pair and the two or three electron pairs of a multiple bond are treated as a single super pair. • When one or more resonance structures can represent a molecule, VSEPR model is applicable. • Decreasing order of repulsive interaction : lp – lp > lp – bp > bp – bp Valence Bond Theory : Given by L Pauling. It explains that a covalent bond is formed between two atoms by overlap of their half-filled valance orbitals, each of which contains one unpaired electron. Orbital Overlap Concept : Formation of a covalent bond results by pairing of electrons in valence shell with opposite spins. Types of Overlapping : (i) Sigma (σ) bond – end to end. (ii) Pi (π) bond – axis remain parallel to each other. Hybridisation : Process of intermixing of orbitals of different energies resulting in formation of new set of orbitals of equivalent energies and shape. Types of Hybridisation –(i) sp (ii) sp2 (iii) sp3 Bonding Molecular Orbitals : Addition of atomic orbitals. Antibonding Molecular Orbitals : Subtraction of atomic orbitals.

Energy required to completely separate one mole of a solid ionic compound into gaseous constituent ions.

.B

A

A .. B

.B

120°

AB4 B

.. B

A

5'

9°

10

B Tetrahedral

BF3

A

B CH4,NH4+

.B.

B:

AB6 90° :B

.. B

:B PCl5

Trigonal bipyramidal

120°

AB5 :B

90°

.B.

.B. Octahedral

A

.. B

B

AB2E

Chemical Bonding and Molecular Structure

.B.

B:

90°

B

SO2,O3

SF6

Bent

A

..

E

Kossel Lewis approach to chemical bonding :

NH3

H2 O B B Bent (Tetrahedral)

:E

A

..

E

B B Trigonal pyramidal (Tetrahedral)

B

A

E

..

A B

B SF4

A E:

E: CIF3 B T–shape(Trigonalbipyramidal)

AB3E2 B

B

B See saw (Trigonalbipyramidal)

AB4E :E

B

B

..

A

B

B

B BrF5

AB4E2

A

B XeF4 B E .. Square planar (Octahedral)

B

B

E

..

E Square Pyramidal (Octahedral)

AB5E

B

* Lewis pictured the atom as a positively charged 'kernel' and the outer shell accommodates a maximum of eight electrons. • Lewis postulated that atoms achieve the stable octet when linked by chemical bonds. • Kossel gave following facts: * In the periodic table, highly electronegative halogens and highly electropositive alkali separated by noble gases. * Formation of a negative ion from a halogen atom and a positive ion from an alkali metal atom is associated with gain and loss of electron by respective atoms. * Negative and positive ions formed attain noble gas electronic configuration. • Negative and positive ions are stabilized by electrostatic attraction. Octet Rule : Atoms can combine either by transfer of valence electrons from one atom to another or by sharing of valence electrons to complete octet in their valence shells. Lewis dot Structure provides a picture of bonding in molecules and ions in terms of the shared pairs of electrons and the octet rule. How To Write A Lewis Dot Structure: Step 1 : Add the valence electrons of the combining atoms to obtain total number of electrons. Step 2 : For anions, each negative charge means addition of one electron. For cations, each positive charge means subtraction of one electron from total number of valence electrons. Step 3 : Write chemical symbols of combining atoms. Step 4 : Least electronegative atom occupies central position. Step 5 : After accounting for shared pairs of electrons, remaining are either utilized for multiple bonding or remain as lone pairs. Formal Charge= (Total number of valence electrons in free atom) – [(Total number of non-bonding electrons) + 1/2(Total number of bonding electrons)] Limitations Of Octet Rule : • Shows three types of exceptions i.e. incomplete octet of central atom, odd-electron molecules and expanded octet. • Does not account for the shape of molecules. • Fails to explain stability of molecules. Hydrogen Bond: Formed when the negative end of one molecule attracts the positive end of other. Types: (i) Intermolecular : Between two different molecules of same or different substances. (ii) Intramolecular : Between two highly electronegative atoms in the same molecule.

AB3E

AB2E2

Postulates : • Electrons in a molecule are present in various molecular orbitals as electrons are present in atomic orbitals. • Atomic orbitals of comparable energies and proper symmetry combine. •Atomic orbitals is monocentric while a molecular orbital is polycentric. • Number of molecular orbitals formed is equal to number of combining atomic orbitals. • Bonding molecular orbitals has low energy and high stability. Types of MO : σ(Sigma), (Pi), δ (Delta)

180° :B BeCl2,HgCl2

Trigonal planar

AB3

AB2 :B

Types : (i) Covalent Bond : A chemical bond formed between two atoms by mutual sharing of electrons between them to complete their octet. (ii) Ionic Bond : A chemical bond formed by complete transfer of electrons from one atom to another acquire the stable nearest noble gas configuration. (iii) Coordinate bond : A chemical bond formed by donation of two electrons from one atom to another to complete their octct.

40 Oswaal JEE (Main) Mock Test 15 Sample Question Papers

rH= rH1+ rH2+ rH3............ rH 1

B

rH2

D

rH 3

is the enthalpy change when one mole of an ionic compound dissociates into its ions in gaseous state.

Applicatio ns

∑bond enthalpies reactants – ∑bond enthalpies products

∆aH is the enthalpy change on breaking one mole of bonds completely to obtain atoms in gas phase.

ΔG = ΔH – TΔS ΔG 0, process is non-spontaneous

Chemical Thermodynamics

° sol H is the enthalpy change when one mole of a substance dissolves in a specified amount of solvent.

If a reaction takes place in several steps then its standard reaction enthalpy is the sum of standard enthalplies of international reactions into which the overall reactions may be divided at the same temperature. rH1 A C

–∑ b H i reactants rH = ∑aiH products i (a) Standard Enthalpy of reactions is the enthalpy change for a reaction when all the participating substances are in their standard states. (b) Enthalpy changes during phase transformations: Standard enthalpy of fusion / molar enthalpy of fusion, fusHθ is the enthalpy change that accompanies melting of one mole of a solid substance in standard state. Standard enthalpy of vaporization or molar enthalpy of vaporization. vapHθ is the amount of heat required to vaporize one mole of a liquid at constant temperature and under standard pressure. (c) Standard molar enthalpy of formation rHθ is the standard enthalpy change for the formation of one mole of a compound from its elements in their most stable state of aggregation.

First Law of Thermodynomics ; Energy can neither be created nor be destroyed but it can be converted from one form to another. Second Law of Thermodynomics: All spontaneous processes are accompanied by a net increase of entropy. Third Law of Thermodynomics: The entropy of a pure and perfectly crystalline substance at the absolute zero temperature is zero.

In calorimetry, the process is carried out in a vessel called calorimeter, immersed in a known volume of a liquid. (a) U measurements: The energy changes are measured at constant volume. No work is done. (b) H measurements: In exothermic reaction, heat is evolved, so qp and rH will be negative. In endothermic reaction, heat is absorbed, so qp and rH will be positive.

Cp - C v = R

∆cH is the enthalpy change per mole of a substance when it undergoes combustion and all reactants and products are in standard state.

Δr H o

Property whose value does not depends on the quantity or size of matter present. (Temperature, density, Pressure etc).

m Te r

y og ol in

Property whose value depends on the quantity or size of matter present in the system. eg. mass Volume Internal energy etc.

ΔSTotal = ΔSsystems + ΔSsurroundings q rev S= T

q=Cxmx T=C T

ΔH is negative: Exothermic reactions. ΔH is positive: Endothermic reactions.

Reversible Process: The process which can be reversed at any moment by an infinitesimal change. Irreversible Process: Processes other than reversible process. At constant temperature Wrev = 2.303 nRT log Vf Vi For adiabatic change, q=0, U = Wad

Vi

Work= –Pex ∆V=–Pex (Vf –Vi) = Pex dV

Vf

•System and Surroundings: A system refers to that part of universe in which observations are made and remaining universe constitutes the surroundings. •Types of System: 1. Open System: There is exchange of energy and matter between system and surroundings. 2. Closed System: There is no exchange of matter but exchange of energy is possible. 3. Isolated System: There is no exchange of energy or matter between the system and surroundings. 4. State of system : Described by its measurable or macroscopic properties. 5. Internal Energy : as a state function: It is the sum of chemical, electrical, mechanical or any other type of energy. 6. (a) Work: Adiabatic process is in which there is no transfer of heat between system and surroundings. ΔU = U2 – U1 = Wad (b) Heat is change in internal energy of a system by transfer of heat from the surroundings to the system or vice-versa without expenditure of work. q is positive: Heat is transferred from surroundings to system. q is negative: Heat is transferred from system to surroundings. (c) General Case First law of Thermodynamics: U = q+W the energy of an isolated system is constant.

Mind Maps

41

En tro py

Mass of solute × 100 Volume of solution

Volume of component × 100 Total volume of solution

s

Molality: Number of moles of solute per kilogram of the solvent

Molecular mass Valency

No. of moles of solute×100 Volume of solution

Molarity : Number of moles of solute in 1L solution

Gas – Solid → O2 in Pd Liquid – Solid → Amalgam of Hg with Na Solid – Solid → Cu dissolved in gold

Gas – Liquid → O2 dissolved in water Liquid – Liquid → Ethanol dissolved in water Solid – Liquid → Glucose dissolved in water

No. of moles of solute×100 Mass of solvent

Gram Equivalents of solute Mass of solute = Equivalent weight Equivalent weight =

Exothermic ∆sol H < 0, Solubility decreases

Endothermic ∆sol H > 0, Solubility increases

Not significant

Increases with decrease in temperature

Gas – Gas → Mixture of O2 and N 2 Liquid – Gas → Chloroform with N2 Solid – Gas → Camphor in N2

No. of gram equivalentof solute×100 Volume of solution

No. of moles of component Total no. of moles of all components

No. of parts of components×10 6 Total no. of parts of components of solution

Mass of component in solution × 100 Total mass of solution

ou se

Normality: Number of gram equivalents of the solute dissolved in one litre of solution

Solutions

Mole fraction

Parts per million : For trace quantities

Mass percentage w/w

Volume percentage v/v

Mass by volume p ercentage (w/v)

Maximum boiling azeotrope

∆H mix = negative ∆Vmix = negative

∆Vmix = positive ∆H mix = positive

For any solution, the partial vapour pressure of each volatile component is directly proportional to its mole fraction.

Non-ideal solution → (Mixture of chloroform and acetone)

Ideal solution → (n-hexane and n-heptane)

Minimum boiling azeotrope

W2 ×M 1 P°1 - P1 = M 2 ×W1 P°1

K b ×1000 × W2 M 2 × W1

K f × W2 ×1000 M 2 ×W1

• Relative lowering of vapour pressure →

• Elevation of boiling point → ∆Tb =

• Depression in freezing point → ∆Tf =

• Osmotic pressure → π = CRT

Increases with increase in pressure

Gas in L iq u id

Normal molar mass = Abnormal molar mass

G a

Partial pressure of gas in vapour phase is proportional to the mole fraction of gas in the solution. p =KHx

42 Oswaal JEE (Main) Mock Test 15 Sample Question Papers

o

Arrhenius Concept: Arrhenius acid: gives H+ ions Arrhenius base: gives OH – ions Bronsted–Lowry Concept: Bronsted –Lowry acid: proton donor Bronsted –Lowry base: proton acceptor form conjngate acid - base pair Lewis Concept: Lewis acid: Electron pair acceptor Lewis base: Electron pair donor

ΔG is negative, reaction is spontaneous and proceeds in forward direction . ΔG is positive, reaction is non-spontaneous and proceeds in backward direction . ΔG is 0, reaction has achieved equilibrium. ° K = e– G /RT

Step 1: Write the balanced equation for the reaction. Step 2: Make a table that lists for each substance involved in reaction; Initial concentration, change in concentration, equilibrium concentration. Step 3: Substitute the equilibrium concentrations into the equilibrium equation for the reaction and solve. Step 4: Calculate equilibrium concentrations from the calculated value of concentration of substances. Step 5: Check results by substituting them into the equilibrium equation. Buffer Solutions: These are the solutions which reside change in pH on dilution or addition of acid or alkali. Solubility Product (Ksp): For a sparingly soluble salt, it is the product of molar concentration of ions raised to power equal to numbers of times each ion.

• If Qc < Kc, net reaction goes from left to right. • If Qc > Kc, net reaction goes from right to left. • If Qc = Kc, no net reaction occurs

• Kc < 10-3 reaction proceeds rarely. • Kc > 103 reaction proceeds nearly to completion • Kc → 10–3 to 103, reaction is at equilibrium

a Reactants and products are in same phase.

Ba

m

Equilibrium Law o r

La w

of

pH of a solution is negative logarithm to base 10 of the activity of hydrogen ion Size increases HF Covalent > H–bonds > Dipole > Vanderwaal 5.

Z2 Energy (E) ∝ 2 n z n

Radius

∝

n2 z2

Chemical Bond Strength

I can't Handle Dirty Vans

Bohr Model of an atom

∝

Diatomic Molecules

Have No Fear of Ice Cold Beer

Lyman (n1=1) Balmer (n1=2) Paschen (n1=3) Brackett (n1=4) Pfund (n1=5)

Velocity

H–bonding

H-bonding is FON (Fun)!

Myan Mer Pasta Bread Fund

7.

Formal Charge

Bond Polarity

SNAP Symmetrical → Non Polar Asymmetrical → Polar 6.

Hybridisation

(VMCA)

( 69 )

Chapter - 6 Solutions

Steric No. = 1/2 [V+M–C+A] V → Valence e– of central atom M → Monovalent atoms (H/X) C → Cationic Charge A → Anionic Charge

Ideal & Non ideal Solutions

HIV

Chapter - 5 Chemical Thermodynamics 1.

Ideal Enthalpy (∆H) ∆H=0 Intermolecular A–A & B–B is Forces same as A–B Volume (∆V) ∆V=0

Process Boring ACT

Peer's Hard Verified Test

Chapter - 7 Equilibrium

Process ISO Bar Adiabatic ISO Choric ISO Therm Const → Pressure (P) Heat (q) Volume (V) Temp (T) 2.

State Function

Bronsted Acid-Base Concept

PVT HUGS

Strong Army, Lost to Carelessly Weak Bandits

Pressure, Volume, Temp, Enthalpy (H), Internal Energy (U), Gibbs free energy (G) Entropy (S) 3.

4.

Strong Acid gives Weak Conjugate Base

I Work Hard

Chapter - 8 Redox Reactions and Electrochemistry

Change in internal energy (U) = Work (w)+Heat (q)

1.

First law of Thermodynamics

Loss of e– is oxidation Gain of e– is reduction

CP–CV = R

2.

Criteria of Spontaneity

Reduction at Cathode

(dH)S,P Calcium > Magnesium > Aluminium > Zinc > Chromium > Iron > Lead > Copper > Mercury (Hg) > Silver > Gold

T

Gibb's Free Energy

5.

Metal activity series

Get High Test Scores

FAT CAT

DG = DH – TDS

Flow of e– from anode to cathode

( 70 )

6.

Metal activity series Amount of Hundred Ceins Balancing Half Cell Steps : (1) Atoms (2) Oxygen (3) Hydrogen (4) Charge

7.

Medium

Solid Sol

Solid

Solid

Solid Sol

Solid

Liquid

Sol

Solid

Gas

Aerosol

Solid

Gel Emulsion

Liquid

Gas

Aerosol

Electro Chemical Series

Gas

Solid

Solid Sol

Priyanka Chopra Sees Movie About Zebra In The Libya Hiring Cobra Studying Algebra

Gas

Liquid

Foam

Chapter - 10 Classification of Elements and Periodicity in Properties 1.

Elements of Atomic No (1-18)

Happy Harry Listen BBC Network Over French Network. Native Magpies Always Sit Peacefully Searching Clear Areas

For Galvanic Cell

H, He, Li, Be, B, C, N, O, F, Ne, Na, Al, Si, P, S, Cl, Ar 2.

Electrolytic Cell

Group I Elements

Little Nasty Kids Rub Cats Fur

LOAP

Lithium (Li), Sodium (Na), Potassium (K), Rubidium (Rb) Caesium (Cs), Francium (Fr)

Loss of e Oxidation Anode Positive –

3.

Group II Elements

Beer Mugs Can Snap Bar's Reputation

Chapter - 9 Chemical Kinetics and Surface Chemistry

Beryllium (Be), Magnesium (Mg), Calcium (Ca), Strontium (Sr), Barium (Ba), Radium (Ra) 4.

Mechanism of Heterogeneous Catalysis

Group III Elements

BAGIT

RAID Program

Boron (B), Aluminium (Al), Gallium (Ga), Indium (In), Thallium (Tl)

(a) Reactant diffusion on surface (b) Adsorption of Reactant (c) Intermediate formation (d) Desorption of product (e) Product leaves the surface 2.

Phase

Liquid

Loss of e– Oxidation Anode Negative

1.

Type of Colloids

Liquid

LOAN

9.

Dispersion

Liquid

Potassium < Calcium < Sodium < Magnesium < Aluminium < Zinc < Iron < Tin < Lead < Hydrogen < Copper < Silver < Gold (Au) 8.

Dispersed

5.

Group IV B Elements

Can Simple Germans Surprise Public Carbon (C), Silicon (Si), Germanium (Ge), Tin (Sn), Lead (Pb)

Types of Colloids

Soft SAGE And Shredded Face (SSAGEASF)

6.

Group V B Elements

New Police Assign Subordinate Bikram on Duty ( 71 )

Nitrogen (N), Phosphorus (P), Arsenic (As), Antimony (Sb), Bismuth (Bi) 7.

(a) Concentration of Ore (b) Isolation (c) Purification

Group VI B Elements

2.

Old Sahranpur Seems Terribly Polluted

Honest Man Feeling Low (HMFL)

Oxygen (O), Sulphur (S), Selenium (Se), Tellurium (Te), Polonium (Po) 8.

(a) Hydraulic Washing (b) Magnetic Separation (c) Froath Floatation Method (d) Leaching

Group VII B Elements

First Class Biryani In Australia

9.

3.

Conversion to Oxide

Fluorine (F), Chlorine (Cl), Bromine (Br), Iodine (I), Astatine (Al)

CRAP

Group VIII B/18 Elements

Calcination → Absence of O2 Roasting → Presence of O2

He never Arrived; Karan exited with Rohan

4.

Ores

MISH Prime Minister Going China

Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), Xenon (Ex), Radon (Rn)

Iron ores → Magnetite, Iron pyrites, Siderite, Haematite Copper ores → Copper pyrites, Malachite, Copper Glance, Cuprite

10. 3d-Series

Scary Tiny Vicious Creatures are Mean females come to Night Club Zen

Chapter - 12 Hydrogen, s & p-Block Elements Hydrogen

Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, 11. 4d-Series

Yes S(z)sir Nob. Most Technicians Rub Rod's Pale Silver Cadillac

1.

Isotopes of Hydrogen

Pro-Diabetic Treatment PDT)

Y, Zr, Nb>Mo, Tc, Ru, Rh, Pd, Ag, Cd 12. 5d-Series

Protium

Late Harry Took Walk, Reached Office In Pajamas After an Hour

1   H 1 

2  Deuterium  H  1 

La......., Hf, Ta, W, Re, OS, Ir, Pt, Au, Hg

Tritium

13. Lanthanides

Ladies Can't Put Needles Properly in Slot-machnies. Every Girl Tries Daily However, Every Time You'd be lose

2.

3   H 1 

H–Bonding

iso FON ! (Say Fun)

La, Ce, Pr, Nd, Pm, Sm, Eu Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu

Fluorine, Oxygen, Nitrogen 3.

Chapter - 11 General Principles and Process of Isolation of Metal 1.

Concentration of Ore

Hardness of Water

CM is temporarily hard with Head Clerks (HC) but permanently Temporary hardness due to Mg(HCO3)2, Ca(HCO3)2

Process of Metallurgy

Permanent hardness due to MgCl2, CaCl2, MgSO4, – 2– CaSO4 Hard with civil servants (CS) Cl , SO

CIP (Read opp PIC) ( 72 )

hydrogen Carbonate (HCO3–)

s-block 4.

elements

Ion

Group I Elements

Mn2+

Little Nasty Kids Ruts Cats Far

Fe2+/Fe3+

Lithium (Li), Sodium (Na), Potassium (K), Rubidium (Rb), Caesium (Cs), Francium (Fr) 5.

Cement Modified Soil (CMS) Oxidised

Green

→

FYG

Grey

→

NBG

Cu2+

Blue

Red

→

CBR

→

CDD

Deep Blue Deep Blue

elements

New Police Assigns Subordinate Bikram on duty Nitrogen (N) Phosphorus (P) Arsenic (As) Antimony (Sb) Bismuth (Bi)

Old Sahranpur Polluted

Sodium ion(Na+) is oxidised ACC → reduced→Anode of carbon on which Cl is reduced –

(Na/Li + liq.NH3) – (Reducing in nature, Paramagnetic, conducting, Coloured)

Seems

Terribly

Oxygen (O) Sulphur (S) Selenium (Se) Tellurium (Te) Polonium (Pu)

Properties of Birch Reagent

Roman People Can Commute (RPCC)

9.

MPC

12. Group 16 Elements

Cathode Mercury (Hg) on which

8.

Yellow

→

11. Group 15 Elements

Castner Kellnar Cell

p-block

Colour less

Brown

Co2+

Beryllium (Be), Magnesium (Mg), Calcium (Ca), Strontium (Sr), Barium (Ba), Radium (Ra)

7.

Pink

Ni2+

p-block

Group II Elements

Beer Mug Can Snape Bar's Reputation

6.

Oxidising Flame Reducing Flame

13. Group 17 Elements

First Class Biryani In Australia

elements

Fluorine (F)

Group 13 Elements

Chlorine (Cl)

BAGIT

Bronine (Br)

Boron (B), Aluminium (Al), Gallium (Ga), Indium (In), Thallium (Tl)

Astatine (At)

Iodine (I)

14. Group 18 Elements

Group 14 Elements

He Never Arrived; Karan exited with Rohan

Can Simple Germans Surprise Public Carbon (C), Silicon (Si), Germanium (Ge), Tin (Sn), Lead (Pb),

Helium (He) Neon (Ne) Argon (Ar)

10. Borax bead Test

Krypton (Kr)

Multiple Program Combined (MPC) for Your Growth (FYG). New Boys Get (NBG) Common Boys Room (CBR) for Combining Desktop Drawing (CDD)

Xenon (Xe)

Chapter - 13 d & f block elements and Coordination Compounds

( 73 )

1.

3d-Series

I Bought Some Copies to Study Fundamental of Chemistry He Nutured Excellence in Necessary Coordination Compounds

Scary Tiny Vicious Creatures are Mean; Females Come to Night Club Zen Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn 2.

I– < Br– < SCN– < Cl– < S2– < OH– < C2O42– < H2O < NCS– < EDTA4– < NH3 < CN– < CO

4d-Series

I– = I

Yes S(z)ir, Nob Most Technicians Rub Rod's Pale Silver Cadillac

Br– = Brought SCN– = Some

Y, Zr, Nb, Mo,Tc, Ru, Rh, Pd, Ag, Cd 3.

Cl– = Copies to

5d-Series

S2– = Study

Late Harry Took Walk, Reached Office In Pajamas After an Hour

F = Fundamental OH– = Of C2O42– = Chemistry

La....... Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg 4.

H2O = He

Lanthanides

NCS– = Nutured

Ladies Can't Put Needles Properly is Slot-machines. Every Girl Tries Daily, However, Every Time You'd be Lose

EDTA4– = Excellence in NH3 = Necessary CN– = Coordination CO = Compounds

La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu 5.

9.

Common League People win Hearts Vice-Versa

Spectrochemical Series

I Bought Some Copies to Study Fundamental of Chemistry. He Nurtured Excellence in Necessary Coordination Compound

(i) CFSE (∆0) < Pairing Energy (P.E) Ligand → Weak field ligand Type of complex → High spin Complex Pairing of e– in t2g orbital

I < Br– < SCN– < Cl– < S2– < OH– < C2O42– < H2O < NC5– < EDTA4– < NH3 < CN– < CO 6.

Pairing of e– Octahedral Complexes

(ii) CFSE (∆0) < Pairing Energy (P.E) 10. Werner's theory

PIcturesque SNow

Common League People win Hearts

Primary valency → Ionisable i.e., Charge on (PIcturesque) Ionisation sphere

CFSE (∆0) < Pairing Energy Ligand → Weak field Type of complex → High spin Pairing of e– in t2g orbital 7.

Secondary valency → Non (SNow) Coordination number

Werner's theory

Ionisable

i.e.,

Chapter - 14 Environmental Chemistry

PIcturesque SNow Primary valency → Ionisable (Charge on Ionisation sphere) Secondary valency → Non Ionisable (Coordination Number) 8.

Pairing of e– Octahedral Complexes

Spectrochemical series

( 74 )

1.

Gases air Pollutants

HOSCN Hydrocarbons, Oxides of Sulphur (SO2, SO3), Carbon (CO, CO2), Nitrogen (NO, NO2)

2.

Chapter - 16 Hydrocarbons and their Halogen Derivatives

Components of Photochemical Smog

O FAN PAN Ozone, Formaldehyde, Acrolein, Nitric oxide, PAN

1.

Queen Elizabeth Second's Navy Commands, Controls

Chapter - 15 Purification, Basic Principles and Characteristics of Organic Compounds 1.

Qiatonary,

Functional group preference order

2.

ASEHA NAKAA Delhi Training Camp

Alkyl (–R) Halogen (–X) Alkoxyl (–OR) Amino (–NH2, NHR, NR2) Hydroxyl (–OH) Amide (–NHCl) Phenyl (C6H5)

No Preference Functional Group

NAHE Nitro, Alkyl / Aryl, Halo, Ethers 3.

4.

3.

Carbon Chain

CURT-I

Meth, Eth, Prop, But

Carbocation Intermediate Unimolecular Reaction Racemic mixture is obtained Two step process Ist order kinetics

3-D Representation

Solid → Towards observer (

6.

4.

)

Chirality

Dashed → Away from observer (IIIII)

CANS

Types of Organic Reaction

Chiral → Non-Super imposable mirror Images

EARS

Achiral → Super imposable Mirror Images

(a) Elimination (b) Addition (c) Rearrangement (d) Substitution

Chapter - 17 Organic Compound Containing Oxygen 1.

Structural Isomerism

TASte → Tollen's test, Aldehyde group, Silver Mirror

(a) Position (b) Functional Group (c) Metamerism (d) Chair

FAAR → Fehling's test, Aliphatic Aldehyde, RedBrown ppt IMLY → Iodoform test, Methyl group linked to O , Yellow ppt –C–

Optical Isomerism

=

GO (a) Geometrical (b) Optical

Detection test

TASte FAAR IMLy

Poor Farmer Managing Crops (PFMC)

7.

SN1 reaction

Monkey Eat Peeled Bananas

So towards Do away

5.

o, p–directing

AHA AHA P

Carboxylic Acid > Sulphonic Acid > Ester > Acid Halides > Acid Amides >Nitrile > Aldehyde > Ketone > Alcohol > Amnes = > = 2.

m-directing Group

( 75 )

2.

Common Names of Carboxylic Acid

Sucrose → Glucose + Fructose

Frog Are Polite, Being Very Courteous

Non-Reducing Sugar 2.

Formic, Acetic, Propionic, Butyric, Valeric, Caproic 3.

PVT TIM HALL

Dicarboxylic Acid

(Phenylalanine, Valine, Threonine, Tryptophan, Isoleucine, Methionine, Histidine, Arginine, Leucine, Lysine)

Oh My, Such Good Apple Pie, Sweet As Sugar 3.

Oxalic, Malonic, Succinic, Glutaric, Adipic, Pimelie, Subric, Azelaic, Sebacic 4.

Rest all Vitamins are water Soluble 4.

Reaction to convert –C– to alkane Clemmen → son → Zn–Hg/HCl

DNA A=T, G≡C

Wolf → Reaction → NH2–NH2/OH–

(2 H–bonds b/w Adenine & Thymine 3 H–bonds b/w Guanine & Cytosine)

Chapter - 18 Organic Compounds Containing Nitrogen

G≡C A=T Also, GCAT

Chapter - 20 Analytical Chemistry and Chemistry in Everyday life

Carbylamine test

PAFSI (Say Pepsi) Primary amine gives Foul smell of Isocyanicle with CHCl3+KOH Amine Smell RNH2+CHCl3+KOH

1.

Artificial Sweetening Agents

ASSA

RNC+KCl+H2O

Coupling Reaction

Aspartame, Saccharin, Sucrolose, Alitame

DSPO DAY (Say, DeSPO DAY)

Also, Assac Sue Ali 2.

Diazonium Salt + Phenol → Orange dye + N2Cl– +

OH

OH

N=N

OH

(orange dye) + N2Cl– +

NH2

H+

Antiseptic & Disinfectants

Bitter Chlor

Diazonium Salt + Aniline → Yellow dye

N=N

NH2 (yellow dye)

Chapter - 19 Polymers and Biomolecules 1.

DNA & RNA

G3Cinema AT 2PM

(to remember regents of reaction)

2.

Fatsoluble Vitamins → Vitamin K, E, D, A

KEDA

Clemmenson and wolf Reaction

Can Zebra Woo Nightingale

1.

Essential Amino Acids

Disaccharides

Non-reducing SGF ( 76 )

Bithionol , Terpineol, Chloroxylenol 3.

Antacids

His Interaction Presented by lime Ran (Say Simran) Interaction of Histamine prevented by limetidine, Ranitidine

MATHEMATICS MIND MAPS & MNEMONICS

t& Po w er Se t

e

bs

Two sets A and B are set to be equal, written as A=B, if every element of A is in B and every element of B is in A. e.g.: (i) A = {1, 2, 3,4} and B = {3, 1, 4, 2}, then A =B (ii) A = {x : x−5 =0} and B = {x : x is an integral positive root of the equation x2 −2x−15=0} Then A= B

A set which has finite number of elements is called a finite set. Otherwise, it is called an infinite set. e .g.: The set of all days in a week is a finite set whereas the set of all integers, denoted by {……−2, −1, 0, 1, 2,……} or {x | x is integers} is an infinite set. An empty set φ which has no element is a finite set is called empty or void or null set.

A set which has no element is called null set. It is denoted by symbol φ or {}. e.g: Set of all real numbers whose square is −1. In set-builder form: {x : x is a real number whose square is −1} In roaster form: { } or φ

Sets and Representations-I

Su

r form

Method or Rule

Roas ter or Tabula

r form uilde Set b

The number of elements in a finite set is represented by n (A), known as cardinal number. Eg.: A = {a, b, c, d, e} Then, n (A) = 5

Representation of Sets

Let A and B be two sets. If every element of A is an element of B,then A is called a subset of B and written as A⊂B or B⊃A(read as ‘A’ is contained in ‘B’ or ‘B contains A’). B is called superset of A. Note: 1. Every set is a subset and superset of itself. 2. If A is not a subset of B, we write A⊄B. 3. The empty set is the subset of every set. 4. Power Set: If A is a set with n (A) = m, then no. of m subset in power set n [P(A)]=2 e.g. Let A = {3, 4}, then subsets of A are φ, {3}, {4}, {3, 4}. Here, n(A) = 2 and number of subsets 2 of A = 2 =4.

Two finite sets A and B are said to be equivalent, if n(A) = n(B). Note: equal set are equivalent but equivalent sets need not to be equal. e.g.: The sets A = {4, 5, 3, 2} and B = {1, 6, 8, 9} are equivalent, but are not equal.

A set having one element is called singleton set. e.g.: (i) {0} is a singleton set, whose only member is 0. (ii) A = {x : 1 0, roots are real and unequal (ii) If b2 – 4ac =0, roots are real and equal (iii) If b2 – 4ac < 0, roots are imaginary

fC om p le xN

um be

Complex Numbers & Quadratic Equations

A

Conjugate of a complex number: For a given complex number z=a+ib, its conjugate is defined as z= a – ib

Real part

A number of the form a+ib, where a,b ∈R and i  1 is called a complex number and denoted by ‘z’. z= a+ib Imaginary part

tio ua q cE ati r d ua fQ o tion Solu

r

n rga

‘i’

d

Re (z)

θ

f so er w Po

t en um ber g m Ar Nu & x e pl

r

Pl

a

P (a,b)

lex mp o of C bra s Alge ber Num

b are given by x   ±

General form of quadratic equation in x is ax2+bx+c=0, Where a , b , c ∈ R & a  0 The solutions of given quadratic equation

(

to

Pola rR ep re

O (ii) Angle θ made by OP with +ve (0,0) direction of X-axis is called argument of z.

2 2 It is denoted by r  z  a  b

Im(z)

ne

If z= a+ib is a complex number (i)Distance of z from origin is called as modulus of complex number z.

erse Inv e v ber ati um lic N p i x t ul ple m M o c of

r

a a –b b there exists a complex number 2 22 + 2 2 i 2 2i 2 , a +b a  ba +ba  b 1 l denoted by – or z , called multiplicative inverse of z zz a b i 2  1  0i  1 Such that: (a  ib) 2 a  b2 a  b2

oo

Real (z)

e

For a non-zero complex number z=a+ib (a  0, b  0),

Let z=x+iy= a+ib ,squaring both sides, we get (x+iy)2= a+ib i.e. x2y2=a, 2xy=b solving these equations, we get square root of z.

π  θ  π .

z  a  ib  r (cos  i sin  ) The argument ‘’ of complex number z = a+ib is called principal argument of z if

and  = arg (z)

r sin

r

· P (a,b)

r ua Sq n

Im (z)

Mo du of C lus om

Let a = r cos  b = r sin  where, r z

ion tat n se Definition of C o mp Num lex ber s

i; r  1 1; r  2 i ; r  3

1; r  0

b a

Re (z)

P (a,b)

Note: If a+ib = c+id ⇔a=c&b=d

4. Division: z1  a  ib  a  ib . c  id z2 c  id c  id c  id  ac  bd   bc  ad   2   2 i 2  2  c d  c d 

(∵ i 2  1)

 (ac  bd )  (ad  bc)i

3. Multiplication: z1 . z2  (a  ib) (c  id )  a (c  id )  ib(c  id )

2. Subtraction: z1  z2  (a  ib)  (c  id )  (a  c)  (b  d)i

1. Addition: z1  z2  ( a  ib)  (c  id )  ( a  c)  i(b d)

Let: z1= a+ib and z1= c+id be two complex numbers, where a,b,c,d ∈R and i  1

z=a+ib is represented by a point P (a,b)

O (0,0)

Im(z)

A complex number z=a+ib can be represented by a unique point P(a,b) in the argand plane

In general, i 4 k  r =

i  1, i 2  1

82 Oswaal JEE (Main) Mock Test 15 Sample Question Papers

adj A

 

Then Adj A=



A11 A21 A31 A12 A22 A32 A13 A23 A33



1 (iv) Area of triangle, ABC= — 2

     

D D D1 ,y= 2 ,z= 3 , where D  0 D D D

d1 b1 c1

a1 d1 c1

a1 b1 d1

d3 b3 c3

a3 d3 c3

a3 b3 d3

Determinants

e op Pr

|A| s of rtie

,then |A|=2 × 4 – 3 × 2 =2

y

y

y

1 — 2

–

–

6 – we take positive value of the determinant because area is positive.

1 — 2

For eg: if (1, 2) , (3, 4) and (–2, 5) are the vertices, then area of the triangle is

x 1 — x 2 x

(vii) if k j or value of |A| remains same

k

j

in |A|, then the

then |A| can be expressed as |B|+|C|.

|A| can be expressed as sum of two or more elements,

(vi) if elements of a row or a column in a determinant

multiplied by B (const.), then |A|gets multiplied by B. (v) if A aij then k A k A

(iv)if each element of a row (or a column) of A is

then |A|=0

(iii)if any two rows (or columns) of A are identical,

then the sign of |A| changes.

(ii)if any two rows (or columns) of A are interchanged,

A are interchanged ie., |A| = |A'|

(i)|A| remains unchanged, if the rows and columns of

For eg. if A

If (x1, y1), (x2, y2 ) and (x3, y3) are the vertices of triangle, Area of

ts Fac

a b c (x) A= d e f then A a(ei –hf)– b(di–gf) + c(dh –ge) g h i

a3 b3 c3

where D= a2 b2 c2 , D1 = d2 b2 c2 , D2 = a2 d2 c2 , D3 = a2 b2 d2

a1 b1 c1

         

then, x =

(ix) a1 x+b1 y+c1 z=d1 , a2 x+b2 y+c2 z=d2 and a3 x+b3 y+c3 z=d3 .

a1 b1 c1 b1 a1 c1 where D= a2 b2 , D1 = c2 b2 , D2 = a2 c2

c a si

(vi) Suppose AX =B be the system of n non-homogeneous linear equations in n variables then  If A 0, then the system of equation is consistent and has a unique solution which is obtained as X=A–1 B  If A 0 and (adj)B=0, then system of equation is consistent and has infinitely many solutions. (vii) Suppose AX =B be the system of n homogeneous linear equations in n variables then  If A 0, then it has only one solution X=0, which is called as trivial solution.  If A 0 then the system has infinitely many solution and is called non-trivial solutions. D2 D1 (viii) If a1 x + b1y =c1 and a2 x+b2 y=c2 then x = D ,y= D , where D  

(v) If matrix A=

a11 a12 a13 a21 a22 a23 a31 a32 a33

x1 y1 1 x2 y2 1 x3 y3 1

[ [

(ii) ad – bc If  a b c d B

 

(iii) AA–1 =A–1 A=1

–1

andA  (i) A = A

(i) if A = [a11]1×1, then |A|= a11 a a A a a –a a (ii)if A = a a then a a a (iii)if A = a a , then|A | a11 ( a22 . a33 – a23. a32 ) a a a a – a12 a21. a33 – a23.a31 a13 a21 a32 – a 22 a 31

Mind Maps

83

th

row

a a a

–

a a a

a a a

,then adj. A

A A A

A A A A

, then M11=4 and A11=(–1)1+1 4=4.

A

(adj.A) b3 y

c3 z

d3 then we can write AX=B,

s

fa

k

k

or

or or

i

m, 1

j

n; i , j a

m×n

Ma

k

bij

cation

k

ul t ipli

trix

M

∀ i and j; i,j,

aij bjk

AC BC, but

. Also, A BC

(always).

AB C, A B C

] then A

[]

m

AC

i.e. if

AB

A is symmetric matrix if A=A' i.e. A'=A. A is skew – symmetric if A= –A' i.e. A'=–A. A is any square matrix, then– sum of a symmetric and A A' A A A' a skew-symmetric matrix. S.M Skew S.M.

Also, (A')' =A, (kA)' =kA', (A+B)' =A'+B', (AB)' =B'A' .

A [

If A=[aij]m n, then its transpose A'= (AT)=[aji]n

and A B C

j 1

[Cjk] =

n

C [cik]m×p ,

If A, B are two matrices of same order, then A B [aij bij ] .The addition of A and B follows: A B B A, A B C A B C ,– A –1 A, k A B k A k B, k is scalar and k I A k A IA , k and I are constants. If A=[aij]m×n and B=[bjk]n×p ,then AB

N

B if, A and B are of same order and aij bij

aij

Zero matrix : All elemants are zero.

Diagonal matrix : All non-diagonal entries are zero i.e Scalar matrix : aij and aij k (Scalar ), i j, for some constant k. Identity matrix : aij and aij =1, i j

m×1

N is given by a a

a a a aij Row matrix : It is of the form a a a 1×n Square matrix : Here, m = n (no. of rows = no. of columns)

Column matrix : It is of the form aij

A=[aij]m n,

or functions having 'm' rows and 'n' columns. The matrix

A matrix of order m n is an ordered rectangular array of numbers

Properties for applying the operations

ns

po se o

s on i t e ra op y ar tri x ent a Elem n a m o

a Tr

d d d – Unique solution of AX=B is X A B A AX=B is consistent or inconsistent according as the solution exists or not. For a square matrix A in AX=B, if then there exists unique solution. (i) A ,then no solution. (ii) A = and (adj. A) B (iii) if A = and (adj.A).B=0 then system may or may not be consistent.

if a1x+b1y+c1z=d1, a2x+b2y+c2z=d2, a3 x a b c x a b c X y where A B a b c z

A

–1

(A ) =A. Inverse of a square matrix exists if A is non-singular i.e.|A| , and is given by

e yp st

pe ra m tions atr ice s

on

–1 –1

then B is called the inverse of A, A =B or B =A ,

Matrices

x at ri m a

–1

in o

of a ma trix

M

it O

–1

A A ,where Aij is the cofactor of aij. A(adj.A)=(adj.A).A=|A|=I, A – square matrix of order 'n' if |A|=0, then A is singular. Otherwise, A is non-singular. if AB = BA = I , where B is a square matrix,

if A

e.g., if A

If elements of one row (or column) are multiplied with cofactors of elements of any other row (or column), then their sum is zero. For e.g., a11 A21 +a12 A22+a13 A33=0.

If A3×3 is a matrix, then |A|=a11. A11 +a12. A12 +a13. A13.

of aij and cofactor of aij is Aij given by Aij = (–1)i+j Mij.

and j column and is denoted by Mij. If Mij is the minor

th

A is the determinant obtained by deleting i

co

f so

D e f ini tio n

rs

d an

r cto fa an d

Minor of an element aij in a determinant of matrix

84 Oswaal JEE (Main) Mock Test 15 Sample Question Papers

n! r !(n  r )!

n

C0+nC2+nC4+..=nC1+nC3+nC5+.....=2n–1

Cr + Cr-1 = n+1Cr

1. The no. of circular permutations of ‘n’ distinct objects is (n-1)! 2. If anti-clockwise and clockwise order of arrangements are not distinct then the no. of circular permutations of n 1 distinct items is (n  1)! 2 e.g.: arrangements of beads in a necklace, arrangements of flower in a garland etc.

n

n

n

be tw ee

Co

n

Permutations and Combinations Per mut ation s of alike Objects

Perm uta tio n

e ipl inc r .) lP P.C ta (F. en g m in nt u o

n! ; 0  r  nn r!(n  r )!

objects are of first kind, p2 objects are of the second kind, ....pk n! objects are of the kth kind is p1 ! p2 ! p3 !… pk !

The no. of permutations of n objects taken all at a time, where p1

s on ati t u rm Pe

io

In particular, r =n n! 1 Cn  n!0! n n Cn-r= Cr

n

n

Ce rta in om b ina tion s

Cr 

n

n! (n  r )!

Pr–1 n-1

at a time, where repetition is allowed is (n)r

(iii) The no. of permutation of n different things taken r

(ii) When a particular object is never taken in each arrangement in n-1Pr

in each arrangement is

(i) When a particular object is to be always included

taken r at a time:

The no. of all permutations of ‘n’ different objects

Pr  n

is denoted by nPr and is given by

taken r at a time, where repetition is not allowed,

The no. of permutations of n different things

distinct objects is called a permutation.

be made by taking some or all of a number of

Each of the different arrangements which can

can be performed in (m+n) ways.

ways respectively, then either of the two events

they can performed independently in m and n

F.P.C. of Addition: If there are two events such that

occurance of the events in the given order is m×n

in n different ways, then the total number of

m different ways, following which another event

The no. of combinations of n different things taken r at a

Fu n of da C

time, denoted by nCr is given by

F.P.C. of Multiplication: If an event can occur in

called a combination.

their arrangements or order in which they are placed, is

of a number of distinct objects or item, irrespective of

Each of different selections made by taking source or all

ns tio i nd

Cr 

Since,

0 2n where n ∈Ν.

]

2 n(4n2–1) 3

(iv) 13+23+33+............+n3= n(n+1)

[

(iii) 12+32+52+...........+(2n–1)2=

(ii) 1+4+7+10 +..........+(3n–2)= n(3n–1)

Basic Facts n(n+1)(2n+1) (i) The sum of square of first n natural number = 6

Ex: Prove that 2n>n for all positive integer n. Solution: Step1: Let P(1):2n>n Step2: When n=1, 21>1.Hence P(1) is true Step3: Assume that P(k) is true for any positive integer k, 2k>k Step4: We shall now prove that P(k+1) is true Multiplying both sides of step(3) by 2 , we get 2.2k>2 k 2k+1>2k 2k+1> k+k 2k+1> k+1 (since k>1) Therefore, P(k+1) is true when P(k) is true Hence, by P.M.I., P(n) is true for every positive integer n . E x am pl e

o.1 N

Step1: Let P(n) be a result or statement formulated in terms of n in a given equation Step2: Prove that P(1) is true. Step3: Assume that P(k) is true. Step4: Using step 3 , prove that P(k+1) is true. Step5: Thus, P(1) is true and P(k+1) is true whenever P(k) is true. Hence,by the principle of mathematical induction, P(n) is true for all natural numbers n.

Som e im p o rta nt r e lat io n

Principle of Mathematical Induction

Steps for Principle of

Induction

Mathematical Induction Proof

Specific Instances to Generalisation e.g.:Rohit eats food. Vikas eats food. Rohit and Vikas are men.Then all men eat food. Statement is true for n=1,n=k and n=k+1, then, the statement is true for all natural numbers n.

Ex : Prove the following by using the principle of mathematical induction for all n’ N:102n–1+1 is divisible by 11. Answer: Let the given statement be P(n), i.e., P(n): 102n–1 +1 is divisible by 11. It can be observed that P(n) is true for n =1 since P(1) = 102.1–1+1=11, which is divisible by 11. Let P(k) be true for some positive integer k, i.e., 102k–1+ 1 is divisible by 11. ∴ 102k–1+1=11m, where m ∈ Ν.....(1) we shall now prove that P(K+1) is true whenever P(k) is true. Consider 102(k+1)–1+1 =102k+2–1+1 =102k+1+1 =102(102k–1+1–1)+1 =102(102k–1+1)–102+1 =102.11m–100+1 =100×11m–99 =11(100m–9) =11r, where r = (100m–9) is some natural number Therefore, 102(k+1)–1+1 is divisible by 11. Thus, P(k+1) is true whenever P(k) is true. Hence, by the principle of mathematical induction, statement P(n) is true for all natural numbers i.e., n.

Exam ple No. 2

Deduction

Generalisation of Specific Instance e.g.: Rohit is a man and all men eat food, therefore, Rohit eats food.

86 Oswaal JEE (Main) Mock Test 15 Sample Question Papers

x

n

n

nn

1

C0x – C x

y

–

n–1

(1+x)–n =1– nx +

n

y

)n l mia no ts i B ien ffic e Co

(a+b

1

n n–1C r

2

Binomial Theorem and its Applications

r

n

(a+b)n

(vii) nCr = n – r+1 n r Cr–1 (viii) nC0nCr+nC1nCr+1+nC2nCr+2+------nCn–rnCn=2nCn–r

n

C02+nC12+nC22+-----+nCn2=2nCn

n

+b

n(n+1)x2 n(n+1)(n+2)x3+-----– 2! 3!

(iv) Taking a=1, b=x, n=–n

–x

x–y

(a+b)n

(a+b)n

n r

an–rbr

(a+b)n,

(a+b)n,

r

a b

n

are

(a+b)n

Mind Maps

87

 a

1

n 1

 a

G2  a  b

2

...... Gn

n 1

 a

 a b

n

 a

n 1

or G1  ar , G2  ar 2 ,  Gn  ar n where r = b

G1  a  b 1

2

2

2

2

n 1

ab 2 ,G  ab and H  A a+b 2 So, G AH or, G2= AH

Let A, G and H be the AM, GM and HM of two given positive real numbers a & b, respectively. Then,

2

numbers, then the numbers are A  A  G

2

• If A.M.: G.M. of two positive numbers a and b is m : n, then a : b = (m+ m – n ( : (m– m – n ( • If A and G be the AM & GM between two positive

In a series,where each term is formed by multiplying the corresponding term of an AP & GP is called Arithmetico‐Geometric Series. Eg: 1+3x+5x2+7x3+… Here, 1, 3, 5, … are in AP and 1, x, x2, … are in GP.

· ·

etr ic M ea n

(G M )

.P.) (G

n

Ar ith me

2

 12  22  32  …  n 2 

6

n  n  1 2n  1

3

3

3

3

3

2

k 1

n

2

• Sum of first ‘n’ odd natural numbers  (2 k  1)  1 3 5  … (2 n 1)  n

n

 n  n  1   n  k 1  2  3 …  n     k   2   k 1  k 1 

• Sum of cubes of first n natural numbers

k 1

k

n

k 1

2

a1  a2  a3  … +an n

A1  a 

2 b  a  n b  a  ba , A2  a  … An  a  n 1 n 1 n 1 or A1= a+ d, A2 = a+2d, …, An = a + nd, ba where d  n 1

n-Arithmetic Mean between Two Numbers: If a, b are any two given numbers & a, A1, A2, .., An, b are in A.P. then A1, A2, …, An are n AM’s between a & b.

AM 

If three numbers are in A.P., then the middle term is called AM between the other two, so if a, b, c, are in A.P., b is AM of a and c. AM for any ‘n’ +ve numbers a1, a2, a3 , …, an is

An A.P. is a sequence in which terms increase or decrease regularly by the fixed number (same constant). This fixed number is called ‘common difference’ of the A.P. If ‘a’ is the first term & ‘d’ is the common difference and ‘l’ is the last term of A.P., then general term or the nth term of the A.P. is given by an = a+ (n−1)d from starting and an=l–(n–1) d from the end. The sum Sn of the first n terms of an A.P. is given by n n S n  [2a  (n  1)d ]  [a  l ] 2 2

Harmonic Progression (HP) For the solution of HP, we should follow below steps Make the reciprocal of each terms of HP Solve by AP method Make the reciprocal of AP result 1 , 1 --------in HP, then eg: if 1a , a+d a+2d a,(a+d), (a+2d)--------will be in AP now nth term of AP, an = a+(n–1)d 1 So, nth team of HP, = a1 = a+(n+)d n Some Important result 2ab If H is the harmonic mean (H) between a&b, then H= a+b If there is n harmonic mean between a&b, then nth ab(n+1) HM(Hn)= na+b

etic Progression (A.P. Arithm )

M ic on rm Ha

ea

tic up Sp Me to ec an ial ter (AM ms Se ) qu o f so en me ces

Su m

Sequences and Series

n io

• Sum of first ‘n’ natural numbers n  n  1 k 1 2  3 … n  2 • Sum of squares of first n natural numbers n

GM AM & s of tities rtie n a e u q o op Pr een tw tw e b

G eo m

Sum of infinite terms of G.P. is given by a a S∞  ; r  1 or, S ∞  ; r 1 1 r r1

The sum Sn of the first n terms of G.P. is given by a (r n  1) a (1  r n ) Sn  r>1or r 0, c >0 If a, b are two given numbers & a, G1, G2, …, Gn, b are in G.P., then G1, G2, G3 … Gn are n GMs between a & b.

Re

lat i o n sh ip b

etw

ee nA

M ,G

M

an dH M

88 Oswaal JEE (Main) Mock Test 15 Sample Question Papers

•

d  sin x   cos x dx

d 1 sec–1 x = , x >1 |x|√x2–1 dx

d  cos x    sin x dx d 1 sin–1 x = ,–1 0,0≤   2π) is the equation of a straight line where the length of the perpendicular from origin O on the line is p and this perpendicular makes an angle α with +ve x-axis. 6. GENERAL FORM: ax +by+ c =0 is the equation of a straight line in a general form. In this case, slope of line = − b

1. POINT-SLOPE FORM: y – y1 = m(x – x1) is the equation of a straight line whose slope is ‘m’ and passes through the point (x1, y1). 2. SLOPE INTERCEPT FORM: y = mx +c is the equation of a straight line whose slope is ‘m’ and makes an intercept ‘c’ on the y-axis. y2  y1 (x x1) is the equation of a straight 3.TWO POINT FORM: y y1 = x2  x1 linewhich passes through (x1, y1) & (x2, y2).

The distance between the points A(x1, y1) and B(x2, y2) is la u m √ (x1–x2)2 +(y1–y2)2 For e nc sta The P(x, y) divided the line joining A(x1 , y) and B(x2, y) in the ratio Di 2 1 my2+ ny1 mx2 + nx1 ; – – y1 = m + n m:n, then x = m + n on – – cti Se ula Note: • (+ve) sign tells the division is internal, but (–ve) signs tells, the m r Fo division is external. • If m = n, then P is the mid-point of the line segment joining A & B.

e gl

If m1 and m2 are the slopes of two intersecting lines (m1m2 1) and  be the acute angle between them m − m2 then tan  = 1 1 +m1 m2

S l o pe Fo A r r ea m ul o f a Tr ia n

ine ht L g i a f Str Equation o ms s for in variou

√ a2 + b 2 3. The foot of ^rd from a pointy (x1,y1) on the line ax + by+c=0 is: –(ax +by +c) [(ar+x1),(br+y1)], where r= 2 1 2 1 a +b

es

1.The image of a point(x1, y1) about a line ax + by+ c =0 is: –2(ax1+by1+c) [(ar+x1), (br+y1)] where, r= a 2 + b2 2. Perpendicular distance from a point(x1,y1) on the line ax+by+c=0 is: ax1 + by1 + c

lin

Perpendicular lines

of bis ec tor s

r Pa

1.When two lines of the slope m1 & m2 are at right angles, the Product of their slope is −1, i.e. , m1m2 = −1. Thus, any line perpendicular to 1 x+d where d is y=mx + c is of the form , y =−m any parameter. 2.Two lines ax + by +c =0 and a’x + b’y + c’=0 are perpendicular if aa’ + bb’ =0. Thus, any line perpendicular to ax + by +c =0 is of the form bx – ay+ k =0, where k is any parameter.

The equation of bisectors of the angles between the lines a1x+b1y+c1=0 and a2x+b2y+c2=0 is given by a1x+b1y+c1 +a2x+b2y+c2 Equ = 2 2 ati a +b √ 1 1 √ a22+b22 on s el all

Len gt h of the fro m p er ap pe o int n on al in e

Angle betwe e n t w o str aigh lines in term t s o f their slop es

1. When two lines are parallel their slopes are equal. Thus, any line parallel to y = mx+c is of the type y = mx +d , where d is any parameter 2. Two lines ax + by +c=0 and a’x + b’y + c’ =0 are parallel if a = b ≠ c a’ b’ c’ 3. The distance between two parallel lines with equations ax +by +c1 = 0 c 1− c 2 and ax +by +c2 = 0 is d= 2 2 a +b

Mind Maps

95

96

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Mind Maps

97

la

23

2  3   3 1



9 5

y

( 95 ,



(

2 5

2 , 1 . 5 5

23

2  4   3  2 

Thus, the required point is

x

z 23

2  5   3  3  

Sol : Let P(x, y, z) be the point which divides line segment joining A (1,–2, 3) and B (3, 4, –5) internally in the ratio 2:3. Therefore,

1 5

eg: Find the coordinates of the point which divides the line segment joining the points (1,–2, 3)and (3, 4, –5) in the ratio 2:3 internally.

cti

respectively.

Coordi id nates of the Centro of a Triangle

Three Dimensional Geometry-I du I n tr o

 mx 2  nx1 my 2  ny1 mz2  nz1   mx 2  nx1 my 2  ny1 mz2  nz1   mn , mn , mn  &  mn , mn , mn     

The coordinates of the point R which divides the line segment joining two points P(x1, y1, z1) and Q(x2, y2, z2) internally and externally in the ratio m : n are given by

rmu n Fo o i t c Se

Sol: Let the coordinates of C be (x, y, z) and the coordinates of the centroid G be (1, 1, 1). Then x  3  1 =1, i.e., x=1; 3 y57 = 1, i.e., y=1; 3 z76 =1, i.e., z=2. So, C (x,y,z) = (1,1,2) 3

eg: The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of A and B are (3, –5, 7) and (–1, 7, –6), respectively, find the coordinates of the point C.

(x2, y2, z2) and (x3, y3, z3) are

 x 1  x 2  x 3 y 1  y 2  y 3 z1  z 2  z 3  , ,   3 3 3  

The coordinates of the centroid of the triangle, whose vertices are (x1, y1, z1),

faM i d po int Co o r d inat es o

nts Two Poi ween e bet tanc Dis

eg:

• Any point on x-axis is : (x, 0, 0) • Any point on y-axis is : (0, y, 0) • Any point on z-axis is : (0, 0, z)

2

2

 x 2  x 1    y 2  y 1    z 2  z1 

2

2

2

 4  1  1  3    2  4 

2

 25  16  4  45  3 5 units

PQ 

Sol: The distance PQ between the points P & Q is given by

eg: Find the distance between the points P(1, –3, 4) and (–4, 1, 2).

PQ 

Distance between two points P(x1, y1, z1) and Q(x2, y2, z2) is given by

• • •

coordinate system are three mutually perpendicular lines. The axes are called x, y and z-axes. The three planes determined by the pair of axes are the coordinate planes, called xy, yz and zx-planes. The three coordinate planes divide the space into eight parts known as octants. The coordinates of a point P in 3D Geometry is always written in the form of triplet like (x,y,z). Here, x, y and z are the distances from yz, zx and yx planes, respectively.

• In three dimensions, the coordinate axes of a rectangular cartesian

 1  4 3  1 4  2  i.e.  3 , 1, 3   2   2 , 2 , 2     

x  x 2 y 1  y 2 z1  z 2  P(x1, y1, z1) and Q(x2, y2, z2) are  1 . , , 2 2   2 eg: Find the midpoint of the line joining two points P(1, –3, 4) and Q(–4, 1, 2). Sol: Coordinates of the midpoint of the line joining the points P & Q are

The coordinates of the midpoint of the line segment joining two points

98 Oswaal JEE (Main) Mock Test 15 Sample Question Papers

on

  b1 , r

 a2

 b2 are coplanar if

point x1 , y1 , z1

to the plane Ax

By

Cz

D

0 is

Ax1 A2

By1 B2

C2

Cz1

The distance of a point with postion  ^   vector a from the plane r . n d is d – a . n . The distance from a

0. Equation of a plane that cuts co-ordinate x y z 1. axes at (a,0,0), (0,b,0), (0,0,c) is a b c

  Two lines r a1     a2 – a1 . b1 b2

D

Equation of a plane

(i) which contains three non-collinear points having position         0. c–a vectors a, b, c is r – a . b – a   (ii) That passes through the intersection of planes r . n1 d1 &      n2 d1 d 2 , – non-zero constant. r . n2 d 2 is r n1

(i) which is at distance 'd' from origin and D.C.s of the normal to the plane as l,m,n is lx+my+nz=d. (ii) rd to a given line with D.Rs. A,B,C and passing through (x1,y1,z1) is A (x–x1) + B (y–y1) +C (z–z1) = 0 (iii) Passing through three non-collinear points (x1,y1,z1) (x2,y2,z2), (x3,y3,z3) is x – x1 y – y1 z – z1 x2 – x1 y2 – y1 z2 – z1 0. x3 – x1 y3 – y1 z3 – z1

(i) two skew lines is the line segment perpendicular to both the lines           (ii) r a1 b1 and r a 2 b 2 is b1 b 2 . a 2 – a 1   b1 b 2 x – x y – y z – z x – x2 y – y2 z – z2 1 1 1 (iii) is and a2 b2 c2 a1 b1 c1 x2 – x1 y2 – y1 z2 – z1 a1 b1 c1 a2 c2 b2 = 2 2 2 b1 c2 – b2 c1 c1 a2 – c2 a1 a1 b2 – a2 b1       b a2 a1     (iv) Distance between parallel line r a1 b and r a2 b is b

x – x1 l1 x – x2 l2

x2 – x1

2

y2 – y1

2

z2 – z1

2

  b .b 1 2 b1 . b2 y – y1 z – z1 and m1 n1 y – y2 z – z2 m2 n2

 b2

l1 l2 m1 m2 n1 n2

a1 a2

b1 b2 a12 b12 c12

c1 c2 a22 b22 c22

Equation of a line through point (x1, y1, z1) and x – x1 y – y1 z – z1 Also, having D.Cs l, m, n is l m n equation of a line that passes through two points is x – x1 y – y1 z – z1 x2 – x1 y2 – y1 z2 – z1

Vector equation of a line which passes through   two points whose position vectors are a and b is     r a b–a

Vector equation of a line passing through the given  point whose position vector is a and parallel to a given     vector b is r a b

cos

between them, then

Angle between t he if l1, m1, n1 , l2, m2, n2 are the D.Cs and a1, b1, c1, a2, b2, c2 two lines are the D.Rs of the two lines and ' ' is the acute angle

to each of the skew lines.

between two intersecting lines drawn from any point (origin) parallel

They lie in different planes. Angle between skew lines is the angle

These are the lines in space which are neither parallel nor intersecting.

are the equations of two lines, then acute angle between them is cos l1 . l2 m1 . m2 n1 . n2

if

then, cos

PQ

line if l, m, n are the D.Cs and a, b, c are D.Rs of a line, then a b c ,m ,n l a 2 b2 c2 a 2 b2 c2 a 2 b2 c2

If ' ' is the acute angle     between r a1 b1 , r a2

Three Dimensional Geometry-II

PQ

D.Rs of a line are the no.s which are proportional to the D.Cs of the

PQ

are x2 – x1 , y2 – y1 , z2 – z1 ,where PQ

then l2 + m2 + n2 = 1. D. Cs of a line joining P (x1, y1, z1) and Q (x2, y2, z2)

positive direction of the co-ordinate axes. If l, m, n are the D. Cs of a line,

D. Cs of a line are the cosines of the angles made by the line with the

Mind Maps

99



 

 





 











a b cos

 

a ×b =0 iff a b















(iv) a  b

a2

b2

b1

j

a1

i

b3

k a3

(iii) a.b=a b1 + a2 b2 + a3 b3 and 1



(ii) a=(a1 )j+(a2)j+(a3)k

  (i) a+b=(a1 b )i+(a 2 b2 )j+(a3 b3 )k 1



If we have two vectors  a a1 i a2 j a3 k , b b1 i b2 j b3 k and is any scalar, then-

a ×(b+c) = a ×b + a×c



a b a b sin n , n is a unit vector perpendicular to line joining a,b. Properties        k (a ×b) =  a ×(k b) a×b= –b ×a





them, then their scalar product a.b  a.b cos. a b

If a, b are the vectors and ' ' is the angle between

 

mb na na mb , (ii) externally is (i) internally is m–n m n to r

Vector Algebra

C

D

B

  if AB , AC are the given vectors,    then AB AC AD

A

adjacent sides are given vectors.

of the parallelogram whose

di

re

x2

y2

on c ti

,

2 14

,

3 14

opp. direction)

if ABC is given triangle, then     AB BC CA 0. B

order is 0 .i.e

A

(vi) Negative of a vector (same magnitude,

C

(v) Equal vectors (same magnitude and direction)

(iv) Collinear vectors (parellel to the same line)

(iii) Coinitial vectors (same initial points)

(ii) Unit vector (magnitude is unity)

sides of a triangle taken in 

14

1

(i) Zero vector (initial and terminal points coincide)

Direction ratios are (1,2,3) and direction cosines are

cosines (l,m,n) of vector ai b j ck are related as: a b c l ,m ,n r  r r eg : If AB i 2 j 3k ,then r 1 4 9 14

The magnitude (r),direction ratios (a,b,c) and direction

respective axes.

ratios, and represent its projections along the

The vector sum of the three

nes cosi

The scalar components of a vector are its direction

and its magnitude is 22 +32 +52 = 38.

OP r

zk and its magnitude is z 2 . eg: Position vector of P (2,3,5) is 2i 3 j 5kˆ

Position vector of a point P (x, y, z) is xi y j

called its magnitude. Magnitude of vector AB is |AB|.

The two coinitial coinitial TheVector vector sum sum of of two vectors is given by the diagonal

s o r d p u r ct of Scala two vectors

The Position vector of a point R dividing a line segment joining P,Q whose position vectors are a, b respectively, in the ratio m : n

ve c

direction of a. eg ‚ if a=5i, then a

i ,which is a unit vector.

5i 5

For a given vector a, the vector a



a gives the unit vector in the a

The distance between the initial and terminal points of a vector is

A quantity that has both magnitude and direction is called a vector.

100 Oswaal JEE (Main) Mock Test 15 Sample Question Papers

n

i=1

Variance of a continuous frequency distribution 1 –2 Var (σ2) = ∑ fi ( xi – x) N

height

,

,

i=1

Standard deviation of a continuous frequency distribution S.D (σ) = 1 N∑ fi xi2 – ( ∑ fi xi)2 N

of n ion t tio ia bu i ev r st D di

S.D.

n f i

i-1

i=1

N

N

i

∑x

Statistics

=

∑ fi

n

•Harmonic Mean (H)

i=1

i (n + 1) team 10 (i – 0.5) Percentile =Pi = 100 n

N

N

N

√

(

f

3N — – 4

(

c

)(

)√

×h

)

( n

x

σ – = b (y–y) – x –x– = r σ (y–y) xy

2

yx

n

2

x 2 x

2 y

y

)

2

)

Mode (for grouped data) M=L +

f1 –f0 ×h 2f1 – f0– f2 Relation among Mean, Median and Mode 3 Median= 2 Mean + Mode

xy

σ ×σ –1( 1–r ) ( θ=tan–1 ( b 1–r ) r +b = tan σ +σ

Angle between two regression lines

x

y

– r σ (x–x) – – = b (x–x) (y –y)= σ yx

Regression equation of y on x.

y

n

1 xi yi – 1 ∑ xi 1 ∑ yi n i=1 n i=1 n∑ i=1

Regression Equations Regression equation of x on y

Here, Cov(x, y) =

Karl Pearson’s Coeff. of correlation n n n n∑ xi yi – ∑ xi ∑ yi Cov (x, y) i=1 i=1 i=1 r= 2 n n n n √Var (x) Var (y) = n∑ xi2 – ∑ xi n∑ yi2 – ∑ yi i=1 i=1 i=1 i=1

Decile: Di =

Q 3 – Q1 Q3 + Q 1

×h , Q3=l+

Coeff. of quartile deviation =

Mean , Me dian ,M ode

N

4

N — –c

f Inter quartile range= Q3–Q1

Quartiles : Q1=l+

Decile tile Perecen

Q ua rti l e s ,D Pe ec r c i l en ea til nd e

n

Var ian c e& a co Sta nt i n n uo da u rd sf re q u en cy

•Geometric Mean (G) n fi log xi ∑ = antilog i-1 n ∑ fi

Mind Maps

101

B

B

A

A

B

A

A–B

AB

AB

s

ly

Ex c lu siv

e hau E v stiv e e n ts ts ven fE o ra eb

Ex

nt

B

Probability-I

S

B–A

Ev

ri xpe

en t

• Simple Event: If an event has only one sample point of a sample space, it is called a ‘simple event’.

sample space ‘S’ is called ‘Sure event’. eg: In a rolling of a die, impossible event is that number more than 6 and event of getting number less than or equal to 6 is sure event.

eg: If an event A= Event of getting odd number in a throw of a die i.e., {1, 3, 5} then , complementary event to A = Event of getting an even number in a throw of a die , i.e. {2, 4, 6} A= {w: w S and wA } = S A (where S is the sample space)

• Complementary Event: Complement event to A = ‘not A’

eg: In rolling of a die, compound event could be event of getting an even number.

• Compound Event: If an event has more than one sample point, it is called a ‘compound event’.

eg: In rolling of a die, simple event could be the event of getting number 4.

m

Probability =

Probability =

3 1  6 2

No.of favourableoutcomes Total no.of outcomes eg: Probability of getting an even no. in a throw of a die. Sol. Here, favourable outcomes = {2, 4, 6} Total no. of outcomes = {1, 2, 3, 4, 5, 6}

Probability is the measure of uncertainty of various phenomenon, numerically. It can have positive value from 0 to 1.

An Experiment is called random experiment if it satisfies the following two conditions: • It has more than one possible outcome. • It is not possible to predict the outcome in advance. Outcome: A possible result of a random experiment is called its outcome. Sample Space: Set of all possible outcomes of a random experiment is called sample space. It is denoted by symbol ‘S’. eg: In a toss of a coin, sample space is Head & Tail. i.e., S= {H,T} Sample Point: Each element of the Sample Space is called a sample point. eg: In a toss of a coin, head is a sample point Equally Likely Outcomes: All outcome with equal probability.

Occurance of event: The event E of a sample space ‘S’ is said to have occurred if the outcome w of the experiment is such that wE. If the outcome w is such that w E, we say that event E has not occurred.

eg: Event of getting an even number (outcome) in a throw of a die.

It is the set of favourable outcomes. Any subset E of a sample space S is called an event.

en

t

De fin itio n

mE Rando

B, AU otA) f o (n

P(A) = P(not A) = 1–P(A)

Pro ba b A  ility B an d P

• Impossible and Sure Event: The empty set  is called an Impossible event, where as the whole

Event A or B or (AB) AB = {w: wA or wB} • Event A and B or (AB) A  B = {w: wA and wB} • Event A but not B or (A–B) A–B = A  B’

•

Many events that together form sample space are called exhaustive events. eg: A die is thrown. Event A = All even outcomes and event B = All odd outcomes. Event A & B together forms exhaustive events as it forms sample space.

Α∩Β

• Probability of the event ‘not A’

U

(As P (A B) = φ)

A–B

A

If A and B are any two events, then • P(AUB) = P(A) + P(B) – P(A B) • P(A B) = P(A) + P(B) – P(AUB) If A and B are mutually exclusive, then P(AUB) = P(A) + P(B) U

Events A & B are called mutually exclusive events if occurance of any one of them excludes occurrance of other event, i.e. they cannot occur simultaneously. eg: A die is thrown. Event A= All even outcomes & event B = All odd outcomes. then, A & B are mutually exclusive events, they cannot occur simultaneously. Note: Simple events of a sample space are always mutually exclusive. U

l ua e M Ev

ut

Al g

102 Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Mind Maps

103

B

c

a

A

b

= s(s–a)(s–b)(s–c) ; here, s=

a+b+c 2

Area of triangle ABC 1 = 12 bc sin A = 12 ca sin B= 2 ab sin C

In, ABC, (i) Sines Law a b c = = sinA sinB sinC (ii) Projection formula (a) a cos C+ c cos A= b (b) b cos A + a cos B= c (c) c cos B + b cos C= a (iii) Cosines Law b2 + c2 –a2 (a) cos A= 2bc a2 +c2 – b2 (b) cos B= 2ac a2 + b2 – c2 (c) cos C= 2ab

∇

sin  = sinn+ (–1)n 

C

cos= 1= 2n, cos= -1= (2n+1)

General solution: The solution consisting of all possible solutions of a trigonometric equation is called its General Solution.  sin= 0  = n , cos = 0=(2n +1) 2 n   tan = 0 = n, sin = sin =n+(–1) , where   ,   2 2 cos = cos = 2n, where [0,]   tan = tan = n+, where   2 , 2    2 2 2 2 sin = sin = n,cos = cos n tan2= tan2= n, sin = 1 =(4n+1)2

o ea

gle ian r T f so tion Solu

l tri ipa me nc Pri = 1ono sin rig T√2

3 , 9 , 11 , . . . .   =  ,  4 4 4 4

e.g.

The equation involving trigonometric functions of unknown angles are known as Trigonometric equations. e.g cos= 0, cos2 –4cos= 1 A solution of trigonometric of n tio the equation is the valueluof o n l S satisfies unknown angle ethat tio ra lu n the equation.& Ge cal So

cos C– cos

C  D  C  D  cos   2  2

CD  C  D  cos    2  2

CD  C  D   sin 2  2

Trigonometric Functions

(

tan2A =

((

(

2 tanA 1  tan2 A sin2A = 2 tan A 1 tan2A 2 cos2A = 1 tan A 1 tan2A sin3A = 3sinA – 4sin3A cos3A = 4cos3A – 3cosA 3A tan3A = 3tan A  tan 2 1 3tan A sin  = 2sin  cos  2 2 cos  = 2cos2  1=12sin2  2 2 tanθ = 2tan  / 1 tan2  2 2

sin2A = 2sinA cosA cos2A = cos2A – sin2A = 2cos2A-1 = 1-2sin2A

n ctio

cot(-θ)=-cotθ

  cos     =±sinθ    tan     =±cotθ    cot     =±tanθ    secθ     =±cosecθ    cosec     =secθ  

sinθ    =cosθ 



cosec(-θ)=-cosecθ

sec(-θ)=secθ

2

cosec ( 2 + ) =+cosecθ

sec ( 2 + ) =secθ

cot ( 2 + ) =+ cotθ

tan ( 2 + ) =+tanθ

cos ( 2 + ) =cosθ

sin( 2 + ) =+ sinθ

cosec (   ) =±cosecθ

sec ( +  secθ

cot ( + ) =+ cotθ

tan ( + ) =+ tanθ

sin( + ) =±sinθ

cos( ( + ) =-cosθ

sec 

3π +  =+ cosecθ  2  3π cosec  +  =secθ  2 

cot 

     =±tanθ   

     =±cotθ   

tan 

cos 

     =+ sinθ   

     =  cosθ   

sin

cosec – cot 1, |cosec  1, R

2

sec2  tan 21, |sec  1, R

sin2 + cos21, –1 sin1, –1 cos1 R

Degree Measure=180   Radian Measure

cos(-θ)=cosθ tan(-θ)=-tanθ



sin2Asin2B=cos2B cos2A=sin(A+B) sin(AB) cos2Asin2B=cos2 B sin2A=cos(A+B)cos(AB)

cot(A±B)=

If in a circle of radius r, an arc of length l subtends an angle of θ radians , then l =rθ.  Degree Measure Radian Measure= 180 

and sum

tan A  tan B 1  tan A tan B

cot A cot B  1 cot A  cot B

tan(A±B)=

sin(A±B)=sinA cosB ± cosA sinB cos(A±B)=cosA cosB  sinA sinB

2sinA sinB=cos(A B) cos(A+B)

2cosA cosB=cos(A+B)+cos(AB)

2cosA sinB=sin(A+B)  sin(AB)

2sinA cosB=sin(A+B)+sin(AB)

sin(-θ)=-sinθ

un lF ica r t e om on g i Tr

C  D  C  D D= –2sin    sin  2  2

cos C+ cos D= 2cos 



sin C – sin D= 2cos 



sin C + sin D =2sin 

lf

Ar

le

sin15° or sin  =√3 1= cos 75°or cos 5 12 2√2 12 cos15° or cos  =√3+1= sin 75°or sin 5 12 2√2 12 √31 =2 √3= cot 75° tan15°= √3+1 √3+1 = 2+√3= cot 15° tan75°= √31  sin or sin 18°=√5  4 10 √5+1 cos  or cos 36°= 4 5

ng

nce of sine and cosine Differe two variables with

Multiple and Ha Angles

fT ria

104 Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Mind Maps

105

• • • •

p implies q is denoted by p  q, then symbol stands for implies, p is a sufficient condition for q.then symbol  p only if q q is a necessary condition for p q implies p

e.g. r: if a number is a multiple of 9, then it is multiple of 3. p: a number is a multiple of 9. q: a number is a multiple of 3. Then, if p then q is the same as following:

• These are statements with word “if then”, “only if ”and “if and only if ”.

The following methods are used to check the validity of statements (i) Direct Method (ii) Contrapositive Method (iii) Method of Contradiction (iv) Using a Counter example

Mathematical Reasoning Se nt

enc e

d un po ent em

ers ifi t n ua

Complement Laws Involution Law ~ (~ A)⇔ A (i) A ∨ (~ A)⇔ T (ii) A ∧ (~ A)⇔ F (iii) ~ T ⇔ F (iv) ~ F ⇔ T Absorption Law (i) A ∨ (A ∧ B)⇔ A (ii) A ∧ (A ∨ B)⇔ A (ii) ~(A ∧ B)⇔ (∼A) ∨ (∼B)

Con and trapo Con sitiv ver e se

Distributive Law (i) A∨(B ∧ C)⇔(A ∨ B) ∧(A ∨ C) (ii) A∧(B ∨ C)⇔(A ∧ B) ∨(A ∧ C) Identity Laws (i) A ∧ T ⇔A (ii) A ∧ F ⇔F (iii) A ∨ T ⇔T (iv) A ∨ F ⇔A

The contrapositive of a statement p  q is the statementq p The converse of a statement p  q is the statement q p e.g. If the physical environment changes, then biological environmental changes. Contrapositive : If the biological environment does not change then the physical environment does not change.  Converse: If the biological environment changes then physical environment changes.

Idempotent Law (i) A ∧ A⇔ A, (ii) A ∨ A⇔ A Associative Law (i) (A ∧ B)∧C⇔ A ∧(B ∧ C), (ii) (A ∨ B)∨ C⇔ A ∨ (B ∨ C) Commutative Law (i) A ∨ B⇔ B ∨ A, (ii) A ∧ B⇔ B ∧ A

Im pl ica t io ns

Q

Co m Sta t

A statement which is formed by changing the true value of a given statement by using the word like ‘no’, ‘not’ is called negation of given statement. • If p is a statement, then negation is denoted by  p e.g. New Delhi is a city. The negation of this statement: It is not the case that New Delhi is a city. It is false that New Delhi is a city. New Delhi is not a city.

A sentence is called a mathematically acceptable statement if it is either true or false but not both. e.g. • The sum of two positive numbers is positive. • All prime numbers are odd numbers. • In above statements, first is ‘true’ and second is ‘false’.

Many mathematical statements are obtained by combining one or more statements using some connecting words like “and”, “or” etc. Each statement is called a “Compound Statement.” e.g. ‘The sky is blue’ and ‘the grass is green’ is a compound statement where connecting word is “and”; the components of Compound Statement are p : The sky is blue q : The grass is green. So, p ∧ q

e.g. For every prime number P, P is an irrational number. • This means that if S denotes the set of all prime numbers, then for all the members of P of the set S, P is an irrational number.

In this statement, the two important symbols are used. • The symbol ‘’stand for “all values of ”; • The symbol ‘’ stand for “there exists”

106 Oswaal JEE (Main) Mock Test 15 Sample Question Papers

MATHEMATICS Chapter - 1 Sets, Relations and Functions Sets And Representations (a)

(iii)

AÚT Û T

(iv)

AÚF Û A

6. Complement Laws -

Today's Scenario, Equally Talented Singers Find Infinite New Songs To Sing.

(i)

AÚ(~A) Û T

(ii)

AÙ(~A) Û F

(iii)

~T Û F

(iv)

~F Û T

7. Absorption Law (i)

AÚ(AÙB)Û A

(ii)

AÙ(AÚB)Û A

(iii) ~(AÙB)Û (–A)Ú(–B) 8. Involution Law (i) Interpretation : Types of Sets : 1. Empty or Null Set - A set which has no element.

~(~A) Û A

Chapter - 2 Complex Numbers and Quadratic Equations

2. Finite Set - A set having finite number of elements.

Iodine Equipment Shows Result Negative One

3. Infinite Set - A set having infinite number of elements.

Square Root

4. Equivalent Set - Two finite sets A and B are said to be equivalent if n(A)=n(B). 5. Equal Set - Two sets A and B are equal if every element of A is in B. 6. Singleton Set - A sets having one element is called singleton set.

(iota)

i = √ –1

Interpretation: Complex numbers are expressed in the form of a+ib where 'i' is an imaginary number called 'iota' and the value of iota is Types of Linear Inequalities

Sets And Representations (b)

Linear Inequality in two variable

Laws of Algebra of Statements : Iacd and Icai are friends

check Train Live Information NDLS

Interpretation : 1. Idempotent Law (i) (AÙA) Û A (ii) (AÚA) Û A 2. Associative Law (i) (AÙB) ÙC Û AÙ(BÙC) (ii) (AÚB) ÚC Û AÚ(BÚC) 3. Commutative Law (i) AÚB Û BÚA (ii) AÙB Û BÙA 4. Distributive Law (i) AÚ(BÙC)Û (AÚB)Ù(AÚC) (ii) AÙ(BÚC)Û (AÙB)Ú(AÙC) 5. Identity Laws (i) AÚT Û A (ii) AÙF Û F

Varanasi Types

Quota SLOT Linear

Variable (or Literal) Slock Quadratic Inequalities

Linear Inequality in one variable Inequalities Numerical Double Literal (or variable) Strict

Interpretation : 1. Numerical Inequality - 34 2. Literal or Variable Inequalities - x8 3. Double Inequality- 50 ïþ

x=

1 ± 17 2

ì

1 - 17 1 + 17 or x ³ í 2 2 ïx > 0 î

again x > 0 ïx £

Þx³

So

= = = =

f ¢(0) + f ¢(2) = e

x2 + x - 4 ³ 0

( -¥ , -a] È [ a , ¥ )

1 + 17 2

...(i)

x = 3

Cont at

x < 0, | x | = -x

-x 2 - 6 + x £ 0



b = c e

Þ

-x 2 - 6 £ | x | £ x 2 - 4 (i)

-1 £ x < 1 1£ x £ 3 3 < x£4

x = 1

Continuous at

-x 2 - 1 - 5 £ | x | £ x 2 + 1 - 5



1 + 17 2

...(ii) (given)

a - b + 2c 2 = e a - b + 4c = e

...(iii)

a - ( ec - ae ) + 4 c = e

from (i)

a - (3ae - ae 2 ) + 12 a = e

from (ii)

2

a{1 - 3e + e + 12} = e 2

e e - 3e + 13 54. (4) Let three terms of G.P. are: a , a , ar r Product = 27 a Þ × a × ar = 27 r Þ a =3 Sum = S a =

Þ Þ Þ

2

a + a + ar = S r 3 + 3 + 3r = S r 3 + 3r = S - 3 r

(given)

136

Oswaal JEE (Main) Mock Test 15 Sample Question Papers Þ



5p 5p ö æ çè cos 12 + i sin 12 ÷ø = (using De Moivre's Theorem) 5p 5p ö æ çè cos 12 - i sin 12 ÷ø

3r 2 - (S - 3)r + 3 = 0 for real r, b 2 - 4 ac ³ 0 (S - 3)2 - 4 ´ 3 ´ 3 ³ 0 S 2 - 6r + 9 - 36 ³ 0 S 2 - 6r - 27 ³ 0 (S - 9)(S + 3) ³ 0

Þ or



-¥ < S ³ -3 9 £ S 0, y > 0 x < 0, y > 0 x < 0, y < 0 x > 0, y < 0

139

Solved Paper-2020

=

1 ( x - y )( x + y - xy ) x-y (1 - x )(1 - y )

=

x + y - xy (1 - x )(1 - y )

66. (2)

2 -1 2 67. (4)   D = 1 -2 l 1 l 1 D = 2( -2 - l 2 ) + 1(1 - l ) + 2( l + 2)

1 / 9 10 - r

Tr +1 =

10

C r ( ax

=

10

C r a10 - r x

)

(b x

-1 / 6 r

)

10 - r r -r bx 9 6

For independent of x 10 - r r - = 0 9 6 10 - r r Þ = 9 6 20 - 2r = 3r r = 4

Let

P =

10

C 4 a 6 b4 ( a 3 + b2 = 4 given)

P =

10

C 4 (4 - b2 )2 b4

a 3 = (4 - b2 )



= 4(4 - b2 )b3 ( -b2 + 4 - b2 ) = 4(4 - b2 )b2 (4 - 2b2 )



For maxima & minima dP = 0 db



Þ



but for b = ±2 Þ

So it is not possible equal to 10k b = 0 Also not possible (So only possible value b = ± 2 ) We have to check second derivative for this but P = a6b4 so there is no need to check it because it is always +ve \ maximum value of P = 10C4 a6 b4 = 210(4 - b2 )2 b4 = 210 ´ 4 ´ 4 = 3360 in equal to 10 given 10 k = 3360 k = 336

= -4 - 2l 2 - 4 - 4 l - 8l + 16 = -2l 2 - 12l + 8

For both -1 l= , & l =1 2 Dx ¹ 0



So no solution for -1 l= , 1 S contains two elements 2 Y = ax + b X = {x Î N :1 £ x £ 17} 17

a 3 = 4 - b2 = 0

= 210(4 - 2) ´ 2

= 2( -2 - l 2 ) + 1( -4 - 4 l ) + 2( -4 l + 8)

68. (3)

b = ±2, 0, ± 2

2



For no solution D = 0 & atleast one of Dx, Dy, Dz ≠ 0 -1 D = 0Þl= ,1 2 2 -1 2 D x = -4 -2 l 4 l 1





= -(2l + 1)( l - 1)

dP = 2(4 - b2 )( -2b)b4 + (4 - b2 )2 4 b 3 db



= -2l 2 + l + 1 = -(2l 2 - l - 1)

T4 +1 =10 C 4 a 6 b4 Should be maximum





= -4 - 2l 2 + 1 - l + 2l + 4

Mean, m =

åY

i

n =1

n 17

=

=

2

=

å ax n =1

+b

i

n 17

17

n =1

n =1

aå xi + å bi n a´

17 ´ 18 + b ´ 17 2 17

17 = 9 a + b 17

Variance =

å (Y - m) i =1

n( n + 1) ö æ ç Sx i = Sn = 2 ÷ø è

i

n

(m = 17 given) ...(i) 2

140

Oswaal JEE (Main) Mock Test 15 Sample Question Papers 17

å ( ax

=

i =1

dy = b , at x = p dx

+ b - 17)2

i

n 17

å ( ax

=

i =1

+ 17 - 9 a - 17)2

i

From Eq.(i)

n 17

å a (x

216 =

2

i =1

i

(Variance = 216 given)

17 17

å (a x

216 =

2

i =1



- 9)2

2 i

- 18 a 2 xi + 81a 2 ) 17

17 ´ 18 ´ 35 18 a 2 ´ 17 ´ 18 a + 81a 2 ´ 17 6 2 = 17 2

216 = 105a - 162 a + 81a 2

2

2

a = ±3 Þ

( a > 0)

Þ b = -10 then a + b = -7 2 + sin x dy = - cos x y + 1 dx

y ( 0 ) = 1,

y ( p) = a

dy - cos x dx = y +1 2 + sin x dy

ò y +1

= -ò

From eq. (ii), 1 dy = 2 dx dy = dx b = Þ a =



cos x dx 2 + sin x

log( y + 1) = - log(2 + sin x ) + C log(1 + 1) = - log(2 + sin 0) + C C = 2 log 2

y( p ) = a Þ log( a + 1) = - log(2 + sin p) + 2 log 2 Þ log( a + 1) = - log 2 + 2 log 2 Þ log( a + 1) = log 2



1 1, b = 1

a+1 = 2 a =1 Again 1 dy -1 cos x = y + 1 dx 2 + sin x

...(i)

and this plane parallel to line 2x = 3 y , z = 1 y z -1 x = = 3 2 0 direction numbers of ^ plane all a, b, c & line direction number's 3, 2, 0 Þ 3a + 2b + 0 c = 0 ...(ii) From eqn. no. (i) & (ii) a-b+c = 0 3a + 2b + 0 c = 0 a +b c = = 0-2 3-0 2+3 = l (let)

...(i)

a = -2l , b = +3l , c = 5l



From eqn. (i), log( y + 1) = - log(2 + sin x ) + 2 log 2

Þ

1

Also passing through (2, 1, 2) a(2 - 1) + b(1 - 2) + c(2 - 1) = 0

y(0) = 1



-( -1) 2+0

a-b+c = 0

a = 3 17 = 9a + b

69. (2)

ìlog( y + 1) = - log(2 + sin x ) + 2 log 2 ü ï ï x=p ï ï í ý log( y + 1) = log 2 + 2 log 2 ï ï ïî ïþ y +1 = 2 Þ y = 1

70. (3) Plane passing through (1, 2, 1) a( x - 1) + b( y - 2) + c( z - 1) = 0

216 = 24a 2

...(ii)

Substituting in eqn. of plane -2l( x - 1) + 3l( y - 2) + 5l( z - 1) = 0 2x - 3 y - 5z + 9 = 0

by option, 3 satisfies it. 71. [9.00]

x 2 + y 2 - 2x - 4 y + 4 = 0 C (1, 2) r =

1+ 4 -4 = 1

3x + 4y = k •

141

Solved Paper-2020

Line 3x + 4y – k = 0 distance from center < radius line 3+8-k 32 + 4 2

M O H, E, R 3 3 2 1 = 18

< 1

M O T E 1 2 1= 2

11 - k < 5

M O T H E R

-5 < 11 - k < 5



-16 < -k < -6 Þ

6 < k < 16

Total = 309 Hence, 309th position

74.[40.00]

k = 7, 8, 9,10,11,12,13,14,15



Total 9 values

72. [2.00]



    | a - b |2 + | a - c |2 =         | a |2 + | b |2 -2 a × b + | a |2 + | c |2 -2 a × c =     1 + 1 + 1 + 1 - 2( a × b + a × c ) =     a ×b + a ×c = The value of     | a + 2b |2 + | a + 2 c |2

8 8 8 -2

...(i)

        = | a |2 + 4 | b |2 + 4 a × b + | a |2 + 4 | c |2 + 4 a × c

    = 1 + 4 + 1 + 4 + 4 (a × b + a × c )

= 10 + 4( -2) = 10 - 8 = 2 73. [309] MOTHER H, E 2 5 4 3 2 1 = 240 M E, H 2 4 3 2 1 = 48

lim



⇒ ⇒



⇒ ⇒

x ®1

( x - 1) ( x 2 - 1) x -1

+

x -1

ò

= = =

2 n = 40

n

x -1

2

0

ò

0

-x + 1 - x dx + ò x - 1 - x dx

ò

1

2

ò

1/2

0

) = 820

x - 1 - x dx

1

0

-1

= 820

2

1

-2 x + 1 dx + ò -1 dx 1

+( -2 x + 1)dx + ò -( -2 x + 1) dx + [ x ]1 1

2

1/2

1/2

1

= éë -x 2 + x ùû + éë x 2 - x ùû + 1 0 1/2 1 1 æ 1 1ö = ç- + ÷ +1-1- + +1 4 2 è 4 2ø 1 1 + +1 4 4 3 = 2 = 1.5 =

(x

1 + 2 + 3 +………+ n = 820 ∑n = 820 n ( n + 1)

75. [1.50]

+ ...... +

JEE (Main) SOLVED PAPER

2019

Time : 3 Hours

Total Marks : 300

General Instructions : 1. 2. 3. 4.

There are three subjects in the question paper consisting of Physics (Q. no. 1 to 30), Chemistry (Q. no. 31 to 60) and Mathematics (Q. no. 61 to 90). There will be only one correct choice in the given four choices For each question 4 marks will be awarded for correct choice, 1 mark will be deducted for incorrect choice and zero mark will be awarded for not attempted question. Any textual, printed or written material, mobile phones, calculator etc. is not allowed for the students appearing for the test. All calculations / written work should be done in the rough sheet is provided with Question Paper.

Physics Q. 1. A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 Nm–1 (see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance 10 W and air drag negligible, N will be close to : XXXX XXXX 10cm B

XXXX XXXX

(1) 1000

(2) 50000

(3) 5000

(4) 10000

Q. 2. A thermally insulated vessel contains 150 g of water at 0°C. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mass of evaporated water will be closest to :

Q. 3. In SI units, the dimensions of

(2) 20 g

(3) 130 g

(4) 35 g

µ0

is :

(1) [A–1 TML3] (2) [AT2 M–1 L–1] (3) [AT–3 ML3/2] (4) [A2T3M–1L–2] Q. 4. A thin circular plate of mass M and radius R has its density varying as r(r) = r0 r with r0 as constant and r is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is I = a MR2. The value of the coefficients a is  : 3 1 (1) (2) 5 2 3 8 (3) (4) 2 5 Q. 5. An alternating voltage v(t) = 220 sin 100pt volt is applied to a purely resistive load of 50 W. The time taken for the current to rise from half of the peak value to the peak value is : (1) 5 ms (2) 2.2 ms (3) 7.2 ms (4) 3.3 ms Q. 6. For the circuit shown, with R1 = 1.0 W, R2 = 2.0 W, E1 = 2 V and E2 = E3 = 4 V, the potential difference between the points ‘a’ and ‘b’ is approximately (in V) : R1

(Latent heat of vaporization of water = 2.10 × 106 J kg–1 and Latent heat of Fusion of water = 3.36 × 105 J kg–1)

(1) 150 g

ε0

.

R1

a

R2

E1

. R1

b

E2

E3 R1

143

Solved Paper-2019 (1) 2.7 (2) 2.3 (3) 3.7 (4) 3.3 Q. 7. In figure, the optical fibre is l = 2 m long and has a diameter of d = 20 mm. If a ray of light is incident on one end of the fiber at angle q1 = 40°, the number of reflections it makes before emerging from the other end is close to : (Refractive index of fiber is 1.31 and sin 40° = 0.64)

Q. 11. Four identical particles of mass M are located at the corners of a square of side ‘a’. What should be their speed if each of them revolves under the influence of other’s gravitational field in a circular orbit circumscribing the square ?

. GM a

(1) 1.35

a

.

.

. (2) 1.16

GM a

GM GM (4) 1.41 a a Q. 12. The wavelength of the carrier waves in a modern optical fiber communication network is close to : (3) 1.21

(1) 55000 (2) 66000 (3) 45000 (4) 57000 Q. 8. The reverse breakdown voltage of a Zener diode is 5.6 V in the given circuit. 200  IZ 9 V— –

800 

The current IZ through the Zener is : (1) 10 mA (2) 17 mA (3) 15 mA (4) 7 mA Q. 9. A boy’s catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms–1. Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to : (1) 106 Nm–2 (2) 104 Nm–2 8 –2 (3) 10 Nm (4) 103 Nm–2 Q. 10. A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of –4Q, the new potential difference between the same two surfaces is : (1) – 2 V (2) 2 V (3) 4 V (4) V

(1) 2400 nm

(2) 1500 nm

(3) 600 nm

(4) 900 nm

Q. 13. Voltage rating of a parallel plate capacitor is 500 V. Its dielectric can withstand a maximum electric field of 106 V/m. The plate area is 10–4 m2. What is the dielectric constant if the capacitance is 15 pF ?

(given e0 = 8.86 × 10–12 C2/Nm2)

(1) 3.8

(2) 8.5

(3) 4.5

(4) 6.2

Q. 14. A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled 3 m is : 3 Force 2 (in N) 1 1 2 3 Distance (in m)

(1) 4 J

(2) 2.5 J

(3) 6.5 J

(4) 5 J

Q. 15. A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule’s heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is :

144

Oswaal JEE (Main) Mock Test 15 Sample Question Papers i 10  E— –

(1)

20 H

2 ln 2

(2)

1 ln 2 2

(3) 2 ln 2 (4) ln 2 Q. 16. Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8 × 102 kg/m3 and specific heat of 2000 J kg–1 K–1 while liquid in B has density of 103 kg m–3 and specific heat of 4000 J kg–1 K–1. Which of the following best describes their temperature versus time graph schematically ? (assume the emissivity of both the beakers to be the same) (1)

60°C T

(2) 60°C

A B

A t

(3)

t

(4) 60°C

60°C T

T

A B

B

T

t

A and B t

Q 17. An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be : (1) 20 cm from the convergent mirror, same size as the object (2) 40 cm from the convergent mirror, same size as the object (3) 40 cm from the convergent lens, twice the size of the object (4) 20 cm from the convergent mirror, twice the size of the object Q.18. A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E = 6 Vm–1 along y-direction. Its corresponding magnetic field component, B would be : (1) 2 × 10–8 T along z-direction (2) 6 × 10–8 T along x-direction (3) 6 × 10–8 T along z-direction (4) 2 × 10–8 T along y-direction

Q. 19. Four particles A, B, C and D with masses mA = m, mB = 2 m, mC = 3 m and mD = 4 m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is  : a

Y

B

a

C

X

a (1) (i − j ) 5 (3) Zero Q. 20.

D

A

a

a

(2) a (i + j ) (4)

A

B

L

L

a   (i + j ) 5



A wire of length 2 L, is made by joining two wires A and B of same length but different radii r and 2r and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire A is p and that in B is q then the ratio p : q is : (1) 3 : 5 (2) 4 : 9 (3) 1 : 2 (4) 1 : 4 Q. 21. A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field Bi ^. The torque on the coil due to the magnetic field is : Br 2 I (1) (2) Bpr2I N πN (3)

Bπr 2 I N

(4) Zero

Q. 22. Two particles move at right angle to each other. Their de-Broglie wavelengths are l1 and l2 respectively. The particles suffer perfectly inelastic collision. The de-Broglie wavelength l, of the final particle, is given by : 1 1 1 (1) = + λ 2 λ12 λ 22 λ + λ2 (3) λ = 1 2

(2) λ =

λ1 λ 2

2 1 1 + (4) = λ λ1 λ 2

145

Solved Paper-2019 Q.23. In an interference experiment the ratio of a 1 amplitudes of coherent waves is 1 = . a2 3 The ratio of maximum and minimum intensities of fringes will be : (1) 2 (2) 18 (3) 4 (4) 9 Q. 24. A 200 W resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be : (1) 100 W (2) 400 W (3) 300 W (4) 500 W Q. 25. Ship A is sailing towards north-east with  ^+ i 50^ j km/hr where ^ i velocity v = 30  points east and ^, j north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will be at minimum distance from B in : (1) 4.2 hrs. (2) 2.6 hrs. (3) 3.2 hrs. (4) 2.2 hrs. Q. 26. The bob of a simple pendulum has mass 2 g and a charge of 5.0 mC. It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equilibrium, the angle that the pendulum makes with the vertical is : (take g =10 m/s2) (1) tan–1 (2.0) (2) tan–1 (0.2) (3) tan–1 (5.0) (4) tan–1 (0.5)

Q. 27. A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1p ms–2, what will be the tensile stress that would be developed in the wire? (1) 6.2 × 106 Nm–2 (2) 5.2 × 106 Nm–2 (3) 3.1 × 106 Nm–2 (3) 4.8 × 106 Nm–2 Q. 28. If 1022 gas molecules each of mass 10–26 kg collide with a surface (perpendicular to it) elastically per second over an area 1 m2 with a speed 104 m/s, the pressure exerted by the gas molecules will be of the order of : (1) 104 N/m2

(2) 103 N/m2

(3) 108 N/m2

(4) 1016 N/m2

Q. 29. Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on He+ ions in n = 1 and n = 2 states. The possible transition of helium ions as they absorb energy from the radiation is : (1) n = 2 → n = 3

(2) n = 1 → n = 4

(3) n = 2 → n = 5

(4) n = 2 → n = 4

Q. 30. Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water = 1000 kg/m3, coefficient of viscosity of water = 1 mPa s) (1) 103

(2) 104

(3) 102

(4) 106

Chemistry Q. 31. Assertion : (A) Ozone is destroyed by CFCs in the upper stratosphere. Reason : (R) Ozone holes increase the amount of UV radiation reaching the earth. (1) Assertion and reason are incorrect. (2) Assertion and reason are both correct, and the reason is the correct explanation for the assertion. (3)  Assertion and reason are correct but, the reason is not the explanation for the assertion. (4)  Assertion is false, but the reason is correct. Q. 32. Adsorption of a gas follows Freundlich adsorption isotherm. x is the mass of the gas

adsorbed on mass m of the adsorbent. The x plot of log versus log p is shown in the m x given graph. is proportional to: m

log

x m

2 3 log p

2/3

(1) p (3) p3

(2) p3/2 (4) p2

146

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 33. An organic compound X showing the following solubility profile is : Insoluble

‘X’

Insoluble Soluble

Q. 39. An organic compound neither reacts with neutral ferric chloride solution nor with Fehling solution. It however, reacts with Grignard reagent and gives positive iodoform test. The compound is : 

(2) Oleic acid

(3) m-Cresol

(4) Benzamide

Q. 34. The correct order of hydration enthapies of alkali metal ions is :

(1) Li+ > Na+ > Cs+ > Rb+

(2) Na+ > Li+ > K+ > Rb+ > Cs+

(3) Li+ > Na+ > K+ > Rb+ > Cs+

(4) Na+ > Li+ > K+ > Cs+ > Rb+ Q. 35. The following ligand is: NEt2 N O

–

–

O

(2)



Insoluble

(1) o-Toluidine

O

(1)

CH3 H

CH3 O

OH O

(3)

C2 H5



(4)

O —CH3

Q. 40. Diborane (B2H6) reacts independently with O2 and H2O to produce, respectively : (1) HBO2 and H3BO3 (2) B2O3 and [BH4]–

(3) B2O3 and H3BO3 (4) H3BO3 and B2O3 Q. 41. For silver CP (J K–1 mol–1) = 23 + 0.01 T. If the temperature (T) of 3 moles of silver is raised from 300 K to 1000 K at 1 atom pressure, the value of DH will be close to :

(1) hexadentate

(2) tetradentate

(1) 62 kJ

(2) 16 kJ

(3) bidentate

(4) tridentate

(3) 21 kJ

(4) 13 kJ

Q. 37. With respect to an ore, Ellingham diagram helps to predict the feasibility of its.

Q. 42. The vapour pressures of pure liquids A and B are 400 and 600 mm Hg, respectively at 298 K. On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The mole fraction of liquids B is 0.5 in the mixture. The vapour pressure of the final solution, the mole fractions of components A and B in vapour phase, respectively are :

(1) Electrolysis

(1) 450 mm Hg, 0.4, 0.6

Q. 36. Maltose on treatment with dilute HC? (1) D – Glucose and D – Fructose (2) D – Fructose (3) D – Galactose (4) D – Glucose

(2) Zone refining (3) Vapour phase refining (4) Thermal reduction Q. 38. Given, that E° O2 /H2 O = + 1.23 V

E° S O2- /SO2- = 2.05 V



E° Br2 /Br = 1.09 V

2

8

4

E° Au2+ /Au = +1.4 V The strongest oxidizing agent is : (1) Au3+ (2) O2 2– (3) S2O8 (4) Br2



(2) 500 mm Hg 0.5, 0.5

(3) 450 mm Hg, 0.5, 0.5 (4) 500 mm Hg, 0.4, 0.6 Q. 43. Which in wrong with respect to our responsibility as a human being to protect our environment ? (1) Restricting the use of vehicles (2) Avoiding the use of flood lighted facilities (3) Setting up compost tin in gardens. (4) Using plastic bags. Q. 44. If solubility product of Zr3 (PO4)4 is denoted by Ksp and its molar solubility is denoted

147

Solved Paper-2019 by S, then which of the following relation between S and Ksp is correct ? 1

1

 K sp  6 (1) S =   144   

 K 7 (2) S =  sp   6912   

1

 K 9 (3) S =  sp   929   

1

 K 7 (4) S =  sp   216   

Q. 45. The major product of the following reaction is :

Q. 48. In order to oxidise a mixture of one mole of each of FeC2O4, Fe2(C2O4)3, FeSO4 and Fe2(SO4)3 in acidic medium, the number of moles of KMnO4 required is : (1) 2 (2) 1 (3) 3 (4) 1.5 Q. 49. Coupling of benzene diazonium chloride with 1-naphthol in alkaline medium will give :

OCH3 Conc. HBr (excess) Heat



(1)

(2)

(3)



(4)

OH

(2)



Br—CHCH3 OH

Br—CH—CH3 Br

(3)

(4)

CH2CH2Br

CH2CH2Br  

Q. 46. The size of iso-electronic species Cl­–, Ar and Ca2+ is affected by : (1) Azimuthal quantum number of valence shell (2) Electron electron interaction in the outer orbitals (3) Principal quantum number of valence shell (4) Nuclear charge

Q. 50. For the reaction 2A + B → C, the values of initial rate at different reactant concentration are given in the table below. The rate law for the reaction is : [A] (mol L–1) [B] (mol L–1)

Q. 47. The major product of the following reaction is : OH Br2(excess )

SO3H

0.05

0.05

0.045

0.10

0.05

0.090

0.20

0.10

0.720

Q. 51. The correct order of the spin-only magnetic moment of metal ions in the following low spin complexes,

OH Br

(1)



(2)

Br

Br

Br

CH Br



Br



SΟ3 H

Br CH

(3)

Initial Rate (mol L–1 S–1)

(1) Rate = K[A] [B]2 (2) Rate = K[A]2 [B]2 (3) Rate = K[A][B] (4) Rate = K[A]2 [B] OH





CH=CH2 Br



(1)

(4)

Br

Br

SO3H

[V(CN)6]4–, [Fe(CN)6]4–, [Ru(NH3)6]3+ and

[Cr(NH3)6]2+ is : (1) Cr2+ > Ru3+ > Fe2+ > V2+ (2) V2+ > Cr2+ > Ru3+ > Fe2+ (3) V2+ > Ru3+ > Cr2+ > Fe2+ (4) Cr2+ > V2+ > Ru3+ > Fe2+

148

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 52. The lathanide ion that would show colour is : (1) Gd3+ (2) Sm3+ (3) La3+ (4) Lu3+ Q. 53. 100 ml of a water sample contains 0.81 g of calcium bicarbonate and 0.73 g of magnesium bicarbonate. The hardness of this water sample expressed in terms of equivalent of CaCO3 is : [Molar mass of calcium bicarbonate is 162 g mol–1 and magnesium bicarbonate is 146 g mol–1] (1) 5,000 ppm (2) 1,000 ppm (3) 100 ppm (4) 10,000 ppm Q. 54. The quantum number of four electrons are given below : I. n = 4, l = 2, ml = – 2, ms = − 1 2

1 II. n = 3, l = 2, ml = 1, ms = + 2

III. n = 4, l = 1, ml = 0, ms = + IV. n = 3, l = 1, ml = 1, ms = −

1 2

1 2



The correct order of their increasing energies will be : (1) IV < III < II < I (2) I < II < III < IV (3) IV < II < III < I (4) I < III < II < IV Q. 55. The major product of the following reaction is : O Br NaBH4 MeOH, 25°C



OMe

Br

(1)

(2)



OMe

(3)

CH3 OH

CH3–CH–CH–CH2–COOH (1) 4,4-dimethyl-3-hydroxybutanoic acid (2) 2-Methyl-5-hydroxypentane-5-oic acid (3) 3-Hydroxy-4-methyl pentanoic acid (4) 4-methyl-3-hydroxypentanoic acid Q. 57. Element ‘B’ forms ccp structures and A occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids. The structure of bimetallic oxide is : (1) A2BO4 (2) AB2O4 (3) A2B2O (4) A4B2O Q. 58. In the following compounds, the decreasing order of basic strength will be : (1) C2H5NH2 > NH3 > (C2H5)2NH (2) (C2H5)2NH > NH3 > C2H5NH2 (3) (C2H5)2NH > C2H5NH2 > NH3 (4) NH3 > C2H5NH2 > (C2H5)2NH Q. 59. Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume nonexpansion work is zero) (1) Cyclic process : q = –W (2) Adiabatic process : DU = –W (3) Isochoric process : DU = q (4) Isothermal process : q = –W

OH

OH



Q. 56. The IUPAC name of the following compound is :

(4)

Q. 60. Which of the following amines can be prepared by Gabriel phthalimide reaction ? (1) n-butylamine (2) triethylamine (3) t-butylamine (4) neo-pentylamine

149

Solved Paper-2019

Mathematics Q. 61. The sum of the co-efficients of all even degree

(

terms in x in the expansion of x + x 3 - 1

(

+ x - x -1 3

) , (x > 1) is equal to : 6

(1) 26

)

6

(2) 24

(3) 32

(4) 29 æ1ö 3 æ ö Q. 62. If a = cos–1 ç ÷ , b = tan–1 ç 3 ÷ ,where 0 < α, è ø è5ø p b < , then a – b is equal to : 2 9 ö æ 9 ö -1 æ (2) cos ç (1) sin -1 ç ÷ ÷ è 5 10 ø è 5 10 ø æ 9 ö -1 æ 9 ö (3) tan -1 ç ÷ (4) tan ç 14 ÷ è ø è 5 10 ø Q. 63. The shortest distance between the line y = x and the curve y2 = x – 2 is : 11 (2) 2 (1) 2 4 7 7 2 (3) (4) 4 8 Q. 64. If a and b be the roots of the equation x2 – 2x + 2 = 0, then the least value of n for n

æaö which ç ÷ = 1 is : èbø (1) 4 (2) 2 (3) 5

(4) 3

Q. 65. Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct? (1) P (A|B) = 1

Q. 68. If S1 and S2 are respectively the sets of local minimum and local maximum points of the function. f(x) = 9x4 + 12x3 – 36x2 +25, x ∈ R, then : (1) S1 = {–2, 1}; S2 = {0} (2) S1 = {–2, 0}; S2 = {1} (3) S1 = {–2}; S2 = {0, 1} (4) S1 = {–1}; S2 = {0, 2} Q. 69. Let y = y(x) be the solution of the differential dy equation, (x2 + 1)2 + 2x(x2 + 1)y = 1, dx p such that y(0) = 0. If ay (1) = then the 32 value of  ‘a’ is : (1)

1 2

(2) 1

1 1 (4) 16 4 Q. 70. Let O (0, 0) and A (0, 1) be two fixed points. Then the locus of a point P such that the perimeter of DAOP is 4, is :

(3)

(1) 9x2 – 8y2 + 8y = 16 (2) 8x2 – 9y2 + 9y = 18 (3) 9x2+ 8y2 – 8y = 16 (4) 8x2 + 9y2 – 9y = 18 Q. 71. Let f : [0, 2] → R be a twice differentiable function such that f “(x) > 0, for all x ∈( 0, 2). If f (x) = f (x)+ f (2 – x) , then f  is : (1) increasing on (0, 2) (2) decreasing on (0, 2) (3) decreasing on (0, 1) and increasing on (1, 2)

(2) P (A|B) ≤ P(A) (3) P (A|B) ≥ P (A) (4) P (A|B) = P(B) – P(A) Q. 66. The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is : (1) 40

(2) 45

(3) 49

(4) 48

ì 2x ü ì (1 - x ) ü is Q. 67. If f(x) = log e í ý ,| x | < 1, f í 2 ý î (1 + x ) þ î (1 + x ) þ equal to : (1) 2f(x)

(2) (f(x))2

(3) 2f (x2)

(4) –2f(x)

(4) increasing on (0, 1) and decreasing on (1, 2) écos a - sin a ù Q. 72. Let A = ê ú , a ∈ R such that ë sin a cos a û é0 -1ù A32 = ê ú . Then a value of a is : ë1 0 û p (1) 0 (2) 16 p p (3) (4) 32 64 Q. 73. If the tangents on the ellipse 4x2 + y2 = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a2 is equal to :

150

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

2 17 64 (3) 17 (1)

Q. 74. lim x →0

sin 2 x 2 − 1 + cos x 2

(2)

4 17

(4)

128 17

equals :

(1) (2) 4 2 (3) 4 (4) 2 2 Q. 75. The magnitude of the projection of the vector 2i + 3j + k on the vector perpendicular to the plane containing the vector i + j + k and i + 2j + 3k , is : 3 (1) 3 6 (2) 2 3 2 Q. 76. The greatest value of c e R for which the system of linear equations, x – cy – cz = 0, cx – y + cz = 0, cx + cy – z = 0 has a nontrivial solution, is : (1) –1 (2) 2 1 (3) (4) 0 2 Q. 77. The contrapositive of the statement “If you are born in India, then you are a citizen of India”, is : (1) If you are a citizen of India, then you are born in India (2) If your are not a citizen of India, then you are not born in India (3) If you are not born in India, then you are not a citizen of India (4) If you are born in India, then you are not a citizen of India Q. 78. A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate, axes will lie only in : (1) 4th quadrant (2) 1st, 2nd and 4th quadrants (3) 1st quadrant (4) 1st and 2nd quadrants Q. 79. The area (in sq. units) of the region A = {(x, y) ∈ R × R / 0 ≤ x ≤ 3, 0 ≤ y ≤ 4, y ≤ x2+ 3x} is : 26 59 (1) (2) 3 6 53 (3) (4) 8 6 (3)

6

(4)

Q. 80. The equation of a plane containing the line of intersection of the planes 2x – y – 4 = 0 and y + 2z – 4 = 0 and passing through the point (1, 1, 0) is : (1) x + 3y + z = 4

(2) 2x – z = 2

(3) x – 3y – 2z = –2 (4) x – y – z = 0 Q. 81. All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is : (1) 180

(2) 175

(3) 162

(4) 160

Q. 82. The length of the perpendicular from the point (2, –1, 4) on the straight line x+3 y−2 z ,  is : = = −7 10 1 (1) greater than 2 but less than 3 (2) less than 2 (3) greater than 4 (4) greater than 3 but less than 4 Q. 83. The sum of the squares of the lengths of the chords intercepted on the circle, x2 + y2 = 16, by the lines, x + y = n, n ∈ N, where N is the set of all natural numbers is : (1) 320

(2) 160

(3) 105

(4) 210

Q. 84. The sum of the solutions of the equation | x − 2| + x to : (1) 12

(

)

x − 4 + 2, ( x > 0 )

is equal

(2) 9

(3) 10

(4) 4 3 5 Q. 85. If cos (a + b) =   , sin (a – b) = and 0 < a, 5   13 π b < , then tan (2a) is equal to : 4 33 63 (1) (2) 52 52 21 63 (3) (4) 16 16 Q. 86. The sum of the series 2.20C0 + 5.20C1 + 8.20C2 + 11.20C3 +....+ 62.20C20 is equal to : (1) 223

(2) 225

(3) 224

(4) 226

Q. 87. The sum of all natural numbers ‘n’ such that 100 0) Q.89. If f(x) = 2 + x cos x p/4 then the value of the integral ò g ( f ( x ))dx -p / 4 is :

æ æ 3 cos x + sin x ö ö -1 ÷÷ ÷÷ , x ∈ Q. 90. If 2y = çç cot çç è cos x - 3 sin x ø ø è then dy is equal to : dx p p (1) – x (2) – x 3 6 p p (3) x – (4) 2x – 6 3

æ pö ç 0, 2 ÷ è ø

Answers Physics Q. No.

Answer

Topic Name

Q. No.

Answer

1

(3)

Magnetic Effects of Current and

2

Topic Name

16

(2)

Properties of Solids and Liquids

(2)

Thermodynamics

17

(2)

Optics

3

(4)

Physics and measurement

18

(1)

Electromagnetic Waves

4

(3)

Rotational Motion

19

(1)

Rotational Motion

5

(4)

Electromagnetic

20

(3)

Oscillations and Waves

6

(4)

Current Electricity

21

(2)

Magnetic

Magnetism

Induction

and

Alternating Currents Effects

of

Current

and

Magnetism 7

(4)

Optics

22

(1)

Dual nature of Matter and Radiation

8

(1)

Electronic Devices

23

(3)

Optics

9

(1)

Properties of Solids and Liquids

24

(4)

Current Electricity

10

(4)

Electrostatics

25

(2)

Kinematics

11

(2)

Gravitation

26

(4)

Kinematics

12

(2)

Communication Systems

27

(3)

Properties of Solids and Liquids

13

(2)

Electrostatics

28

(1)

Kinetic Theory of Gases

14

(3)

Work, energy and power

29

(4)

Atoms and Nuclei

15

(3)

Electromagnetic

30

(2)

Properties of Solids and Liquids

Induction

Alternating Currents

and

152

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Chemistry Q. No.

Answer

Topic Name

Q. No.

Answer

31

(3)

32

(1)

33

(2)

Analytical Chemistry and Chemistry

34

(3)

35

(2)

Topic Name

Environmental Chemistry

46

(4)

Periodicity of Elements

Chemical Kinetics and Surface

47

(4)

Organic Compounds Containing Oxygen

48

(1)

Some Basic Concepts in Chemistry

Alkali Metal

49

(1)

Organic Compounds Containing Nitrogen

D & F – Black Elements, and

50

(1)

Chemical Kinetics and Surface Chemistry

Chemistry in Every Day Life

Coordination Chemistry 36

(4)

Polymers and Biomolecules

51

(2)

D & F – Black Elements, and Coordination

37

(4)

Principles and Processes of

52

(2)

D & F – Black Elements, and Coordination

38

(3)

Redox Reactions and Electrochemistry

53

(4)

Some Basic Concepts in Chemistry

39

(4)

Organic Compounds Containing

54

(3)

Atomic Structure

Chemistry Metallurgy

Chemistry

Oxygen 40

(3)

Some Basic Concepts in Chemistry

55

(4)

Organic Compounds Containing Oxygen

41

(1)

Chemical Thermodynamics

56

(3)

Purification, Basic Principals and

42

(4)

Solutions

57

(2)

States of Matter

43

(2)

Environmental Chemistry

58

(3)

Organic Compounds Containing Nitrogen

44

(2)

Equilibrium

59

(2)

Chemical Thermodynamics

45

(2)

Organic Compounds Containing

60

(1)

Organic Compounds Containing Nitrogen

Characteristics of Organic Compounds

Oxygen

Mathematics Q. No.

Answer

61

(2)

Topic Name

62

(1)

Trigonometry

63

(3)

Limit, Continuity and Differentiability

78

(4)

Coordinate Geometry

64

(1)

Complex Numbers and Quadratic Equations

79

(2)

Integral Calculus

65

(3)

Statistics and Probability

80

(4)

Three Dimensional Geometry

66

(4)

Statistics and Probability

81

(1)

Permutations and Combinations

67

(1)

Sets, Relations and Functions

82

(4)

Three Dimensional Geometry

68

(1)

Limit, Continuity and Differentiability

83

(4)

Coordinate Geometry

69

(3)

Differential Equations

84

(3)

Solutions of Equation

70

(3)

Coordinate Geometry

85

(3)

Trigonometry

71

(3)

Limit, Continuity and Differentiability

86

(2)

Binomial Theorem

72

(4)

Matrices and Determinants

87

(3)

Properties of Numbers

73

(1)

Coordinate Geometry

88

(3)

Integral Calculus

74

(2)

Limit, Continuity and Differentiability

89

(1)

Integral Calculus

75

(4)

Vector Algebra

90

(3)

Limit, Continuity and Differentiability

Binomial Theorem and its Simple

Q. No.

Answer

76

(3)

Topic Name Matrices and Determinants

77

(2)

Mathematical Reasoning

Application

JEE (Main) SOLVED PAPER 2019 ANSWERS WITH EXPLANATION

Physics 1. (3)

Given : Length of strip is l = 10 cm, resistance of the U shaped wire is negligible, spring constant of spring connected to the strip is k = 0.5 N/m, magnitude of applied magnetic field is B = 0.1 T, mass of strip is m = 50 g, resistance of strip is R = 10 W, number of oscillations performed by the strip before its amplitude decreases by a factor of e is N when pulled from its equilibrium position and released. XXXX XXXX XXXX XXXX ma

To find : Value of N. When the strip is pulled from its equilibrium position, there are two forces acting on the strip which try to bring it back to its equilibrium position, as shown in the above diagram. So,  –kx – FB = ma  (FB = – Bil, is the force due to magnetic field) –kx – Bil = ma

Blv is the current through the strip and R

v is its velocity]

−kx −

= v Put



B2 l 2 v = ma R



dx d x = ,  a in the equation above. dt dt 2

 

2 × 10 × 50 × 10 −3 = 10000 s (0.1)2 × (10 × 10 −2 )2 Time period of oscillation of spring :

 d2x  B 2 l 2  dx  m =  2  R  dt   dt 

 d 2 x  B 2 l 2  dx  m 2 + + kx = 0 R  dt   dt  Above equation is equation of a damped simple harmonic motion, with amplitude :

m 50 × 10 −3 2π = ≈ 2 s k 0.5 So, total number of oscillations in time t :

T = 2π

N= t= 10000= 5000 T 2 2. (2)

Given : Total mass of water in thermally insulated vessel is M = 150 g, temperature of water in vessel is T = 0°C, latent heat of vaporisation of water is L V 2.10 × 10 6 J kg −1 =

latent heat of fusion of water is L F 3.36 × 10 5 J kg −1 . =

2

−kx −

Put the given values :

= t

kx, FB

[ i =

B2 l 2 t =1 2Rm 2Rm t= 2 2 Bl

10cm B

 B2 l 2  A(t ) A 0 exp  − = t 2Rm   A Put A(t ) = 0 in the above equation. e  B2 l 2  A0 t A 0 exp  − = e  2Rm 



To find : The mass of evaporated water when the vessel is pumped out adiabatically. Let mass of evaporated water be x g= x × 10 −3  kg.

So, heat lost by freezing water (amount of water that turns into ice) = heat gained by the evaporated water (amount of water that turns into steam). (150 – x) × 10–3 × 3.36 × 105 = x × 10–3 × 2.10 × 106

154

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

150 × 3.36 × 105 = (2.10 × 10–6 + 3.36 ×10–5)x x  20g ε0 µ0

3. (4)

Given :



To find : Dimension of

ε0 in SI units. µ0



Unit

of

of

permittivity

free

space,

2

c ; (by Coulomb’s law), m2 N Reduce the unit, to get dimensional formula of [e0] = [M–1L–3T4A2]...(i) ε0 =

Also,

ε0 ε 02 = = c ε 0 ...(ii) µ0 ε0 µ0  1  as, c =  ∈0 µ 0 



   

ε0 will µ0 be dimensions of c times dimensions of e0 : ε0 = [c] [e0] µ0

From (i) and (ii) the dimensions of

= [L1T–1] [M–1L–3T4A2] = [M–1L–2T3A2] 4. (3)

Given : Density of circular plate of mass M and radius R varies as r(r) = r0r, where r0 is a constant and r is the distance from the centre, The moment of inertia about an axis perpendicular to the plate and passing through its edge is I = aMR2. To find : Value of coefficient a in, 2 I = aMR . R



= 2pr0 x4 dx...(i) Moment of inertia of this ring about an axis perpendicular to the plate and passing through its edge will be : dIx = dmx2 + dmR2 = 2pr0x4 dx + r0 x(2px dx) R2 = 2pr0 x4 dx + 2pr0 x2 R2 dx ...(ii) Moment of inertia of the complete plate about an axis perpendicular to the plate and passing through its edge will be :

R

0

2 πρo  [ x 5 ]0R 2 πρo  R 2 [ x 3 ]0R + 5 3 16 5 I = πρo R ...(iii) 15 Mass of the ring :



I =

M = ∫dm

= ∫ρo x(2πx  dx )

2 πρo R 3 ...(iv) 3 Equation (iii) can also be written as : 8 2  I = ×  πρo R 3  R 2 5 3  8 = MR 2 ...(v) 5 On comparing equation (v) with I = aMR2, we get : 8 a = . 5 R

2 πρo ∫ x 2 dx= = 0

5. (4) 



As shown in the diagram above consider a ring of radius x and thickness dx. Moment of inertia of this ring about an axis perpendicular to the plate and passing through its centre will be : dlxc = dm × x2 = r0 x(2px dx) × x2

R

0

4 2 2 = ∫ (2πρo x ) dx + ∫ 2πρo x R dx

axis x

I =  ∫dI x







Given : Load resistance is R = 50 W, applied voltage is = V(t ) 220 sin (100 πt ). ...(i) To find : t′, the time taken for the current to rise from half of the peak value to the peak value. Current through the AC circuit at time t : V 220 I(t= ) sin (100 πt ) = R 50 22 I(t ) sin (100 πt ) ...(ii)  = 5 Time period for one complete cycle of current : 2π 2π 1 T s ...(iii) = = = ω 100 π 50

155

Solved Paper-2019

Time period to reach the peak value of current : T 1 s ...(iv) tpeak = = 4 200 Let the peak value of current through the circuit be Ipeak.





So, half the peak value of current will be : I peak . 2 Let time taken by the current to reach half its peak value be t1. So from equation (i), I peak = I peak sin (100 πt1 ) 2 π 100 πt1 = 6 1 ...(v) t1 = 600



From equation (iv) and (v), time taken for the current to rise from half of the peak value to the peak value : 1 1 1 t′ = − = = 3.3 ms 200 600 300

6. (4)

Given : for the circuit below, R1 =1.0 Ω, R 2 =2.0 Ω, E1 =2 V ,

E= E= 4 V. 2 3



R1

.

E1

.

.



2V 4V

1 sin 40°, 1.31 θ2 =29.39

sin θ2 =

θ= 90 − θ= 90 − 29.39= 60.6 2 (q is as labelled in the diagram) x = tan θ tan = 60.6 d (x is labelled in the diagram) x = (20 × 10 −6 ) tan 60.6 =  35.5 µm

8. (1)

Total number of reflections; l 2 m n = = = 56338. x 35.5 µm Given : reverse breakdown voltage of a Zener diode connected as shown in the circuit below is VZ = 5.6 V. 200 

2 2

.

9 V— –



2

2 4 4  2 + 2 + 2  10   = 3.3 V R eq I= = eq 1 1 1 3 + + 2 2 2

IZ

800  I2

To find : The current IZ through the zener diode. Voltage drop cross the Zener diode : VZ = 5.6 V



Voltage drop across the R2 = 800 W resistor : VZ = 5.6 V



Current through the R2 = 800 W resistor : VZ 5.6 I2 = = = 7 mA R 2 800



Voltage drop across the R1 = 200 W resistor : V1 =V − VZ =9 − 5.6 =3.4 V

b

4V

Given : Length of optical fibre, l = 2 m, diameter of the fibre, d = 20 mm, angle of incidence at the entrance of fibre q1 = 40°, refractive index of fibre, m2 = 1.31. To find : Total number of reflections within the fibre. Snell’s law : sin θ2 µ1 , (µ1 is refractive index of air) =   sin 40° µ2

I1

a

Vab=



R1

E2

To find : The potential difference between point a and b. The above circuit can be viewed as a parallel combination of three cells.





b

R1





E3

R2





R1

a

7. (4)

156

Oswaal JEE (Main) Mock Test 15 Sample Question Papers Current through the R1 = 200 W resistor : V1 3.4 = I1 = = 17 mA R1 200



Current IZ through the Zener diode : I Z = I1 − I 2 = 17 − 7 = 10 mA

9. (1)

Given : Length of the rubber cord of the catapult is L = 42 cm, mass of cord is negligible, diameter of cross section of cord is D = 6 mm = 0.006 m, mass of stone is m = 0.02 kg,





The boy pulls the catapult by a length = DL = 20 cm, the initial velocity of the stone when it leaves the catapult is v = 20 m/s. To find : The Young’s modulus of the rubber cord. Potential energy stored by the stretched rubber cord :

1  ∆L  ( ∆L )  D 2 ...(i) Y AL  = 1 Y  π    2  L  2 L 2 In equation (i), A is the area of cross section of the cord with diameter D. The potential energy stored in the stretched cord is given to the stone as kinetic energy. Kinetic energy of stone 2

1 mv 2 ...(ii) = 2





+Q











2

1 × 0.02 × 20 × 20 2 Y ≈ 106 N/m2 10. (4) Given : Charge on solid conducting sphere is Q, charge on the surrounding conducting spherical shell is 0, the potential difference between the two spherical surfaces is V. To find : What will be the new potential difference between the two spherical surfaces if the shell is given a charge –4 Q. Let a be the radius of solid conducting sphere and b be the outer radius of the surrounding conducting spherical shell.

b

(i)

1 ( ∆L )  D  1 Y  π   = mv 2 2 L 2 2   Put given values in the above equation. 1 0.2 × 0.2 × π× 0.006 × 0.006 Y 2 0.42 × 4 =

a

b





+Q

a

As energy is always conserved, equate equations (i) and (ii), 2



2

–4Q

(ii)

For diagram (i) : Potential at the surface of solid conducting sphere is   kQ 1 Vs  is a constant  = = k a 4 π εo   Potential at the surface of surrounding conducting spherical shell : kQ Vsh = b So, potential difference between two spherical surfaces is : 1 1 V = Vs − Vsh = kQ  −  a b For diagram (ii) : Potential at the surface of solid conducting sphere is kQ k (4Q) V= 's − a b Potential at the surface of surrounding conducting spherical shell : kQ k (4Q) V= 'sh − b b So, potential difference between two spherical surfaces is :  kQ k (4Q)   kQ k (4Q)  V 's − V 'sh =  − − − = V b   b b   a

11. (2) Given : Mass of four identical particles placed at the corners of a square = M, Edge length of square = a, the particles revolve in a circular path under the influence of each other’s gravitational field. To find : The speed of particles. A 45°

D

C

B

157

Solved Paper-2019

Net force on particle of mass M located at position B will be towards the centre of the circle: Fnet = FBD + FBA cos 45° + FCA cos 45° =

GM 2

( 2a )

2

+

GM 2  1  GM 2  1   + 2   a2  2  a  2





Body diagonal BD of square

2 a. =

GM 2  1   2 + 2  ...(i) 2 a   The net force acting on particle located at B is represented by equation (i). It is acting as a centripetal force. Mv 2 GM 2  1  =  + 2   a a2  2  2 (distance of location B from centre of square a is ) 2 GM  1  + 1 ; v2 =  a 2 2 

Fnet =

v = 1.16

GM a

12. (2) Given : Modern optical fibre communication network. To find : Wavelength of carrier waves in the network. In modern optical fibre communication network, the signals are transmitted by waves of wavelength l = [1310 – 1550] nm. 13. (2) Given : Voltage rating of a parallel plate capacitor is V = 500 V, di-eletric strength of its dielectric is E = 106 V/m, area of the capacitor plate is A = 10–4 m2, capacitance of the capacitor is C = 15 pF, ε= 8.86 × 10 −12 C 2 / Nm 2 .  o To find : K, dielectric constant of the dielectric material placed between the plates of the given capacitor. Capacitance of a parallel plate capacitor : ε KA C = o d Cd K = ...(i) εo A d in equation (i) is the distance between the plates of the capacitor.



In terms of applied voltage and the dielectric strength : V d = ...(ii) E Substitute from equation (ii) in equation (i) : C V K = ...(iii) ε o A  E  = K

15 × 10 −12  500  ×  6  ≈ 8.5 −12 −4  8.86 × 10 × 10  10 

14. (3) Given : Variation of force acting on a particle as function of distance travelled by it. C

3 Force 2 A (in N) 1

B

D

F E 0 1 2 3 Distance (in m)

To find : kinetic energy of particle at x = 3 m. Work done by the force on the particle will be area under the curve ABC, DW =  Area of square ABEO + area of rectangle BDFE + area of triangle BCD

1  (2 × 2) + (2 × 1) +  × 1 × 1  = 2  1 = 4 + 2 + 6.5 J = 2 By work energy theorem : Kf – Ki = DW = 6.5 J 15. (3) Given : For an LR circuit shown below, L = 20 H, R = 10 W. To find : t′, the time at which rate of dissipation of energy across resistance is equal to the rate at which magnetic energy is stored in the inductor. i 10 



E— –



20 H

Current through the LR circuit : E 1 − e − Rt / L = i R

(



)

Energy stored in the inductor : 1 2 UL = Li 2

...(i)

158

Oswaal JEE (Main) Mock Test 15 Sample Question Papers



Rate at which energy is stored in the inductor : dU L 1 di di = = L (2i ) Li ...(ii) dt 2 dt dt



Rate at which energy is dissipated by the resistor : dU R = i2R ...(iii) dt

At t = t′ : dU L dU R = dt dt di Li = i2R dt

d dt

)

Put t = t′. R − Rt ′ / L e= L e

− Rt ′ / L

=

e − Rt ′ / L =

R 1 − e − Rt ′ / L L

(

− Rt ′ / L

)

)

)

1 2

Rt′ = ln 2 L  

L t′ = ln 2 R = t′

dQ h (T − To ) = dt ms h (T − To ) = Vρ s

20 ln 2 2 ln 2 = 10



Density of liquid in beaker B is





for the entire cooling process. So, graph of B will always lie above graph of A as shown in option b.

17. (2)

f = 10 cm

f = 10 cm I2

object

40 cm

20 cm

I1

I3 40 cm



Specific heat of liquid in beaker A is

Specific heat of liquid in beaker B is

dQ A 1 ∝ ;  800 × 2000 dt dQ A ∝ 6.25 × 10 −7 ...(ii) dt From equation (ii) and (iii) we can see : dQ dQ B   A > dt dt



rB = 103 kg/m3, SA = 2000 J kg–1 K–1,

Put given values in equation (i),



rA = 8 × 102 kg/m3



dQ is rate of cooling, dt

of liquid, s is specific heat of liquid, T is temperature of liquid, T0 is temperature of surrounding, V is volume and r is density of the liquid. As for both the liquids in beaker A and B, h, V, T and T0 are constants : dQ A 1 dQ B 1 ...(i) ∝ ; ∝ ρA sA dt ρ B sB dt



16. (2) Given : Initial temperature of both the beakers A and B is T = 60°C Volume of liquids in both the beakers is same, V = VA = VB Density of liquid in beaker A is



In the above equation :

...(iv)

(

(1 − e



h is heat transfer coefficient, m = Vr is mass

Put value of i from equation (i). R E E − Rt / L  − Rt / L R 1− e  = L × R 1−e  

(





di R = i dt L

J . kg.K To find : Choose the correct cooling graph for both the liquids. Newton’s law of cooling :

SB = 4000



Given : Distance of object from lens is u1 = 40 cm, focal length of the lens f1 = 20 cm, focal length of the mirror f2 = –10 cm, distance between the mirror and the lens d = 60 cm. To find : Location and magnification of the final image.

159

Solved Paper-2019







Location (v1) and magnification (m1) of the image from convex lens : 1 1 1 1 1 1 = − = − = , v1 = 40 cm, v1 f1 u1 20 40 40  m = 1

v   1 1. = u1

The first image is formed at v1 = 40 cm behind the lens and is of same size as object but inverted (I1), which acts as an object for concave mirror. For second image : u2 =  −20 cm, f2  =  −10 cm. Location of image from concave mirror : 1 1 1 1 1 1 = − = − = − ,  v2 f2 u2 −10 −20 20 v2 v2 = −20 cm, m2 = = 1. u2 So, second image is formed at v2 = –20 cm in front of concave mirror, which is same size as object but inverted (I2), which acts as object for lens. For image three (final image I3), u3 = 40 cm, f1 = 20 cm. Location of final image : 1 1 1 1 1 1 = − = − = ,  v3 f1 u3 20 40 40 v= 3

u3 40 cm,  m= = 1. 3 v3

So, final image is formed at v3 = +40 cm in front of the lens, at the same position as object but real and inverted. The image is of same size as that of the object.

18. (1) Given : Direction of propagation of an electromagnetic wave is along the x-axis, the electric field component of the wave at a particular point of space and time is  V E = 6 , j . m  To find : B, the magnetic field  component corresponding to the given E. For an EM wave :  E  = c ;  B  E  6 B = = = 2 × 10 −8  T 8 c 3 × 10



Also, direction of propagation of an EM   wave = direction of E × direction of B,  i = j × direction of B  That gives, direction of B is along the z-axis. So,  B= 2 × 10 −8  k  T 19. (1) Given : mA = m, mB = 2 m, mC = 3 m and mD = 4 m...(i) a = −ai, a = + a j , a = + ai  A

B

C

and aD = −a j ...(ii) To find : Acceleration of centre of mass of the particles, aCM. Acceleration of centre of mass for a system of masses is given as : m a + mB aB + mC aC + mD aD aCM =   A A ...(iii) mA + mB + mC + mD Putting values from equations (i) and (ii) in equation (iii), −mai + 2ma j + 3mai − 4 ma j aCM =   m + 2 m + 3m + 4 m  2mai − 2ma j = 10m a  aCM = (i − j ) 5

20. (3) Given : Total length of wire is 2 L, length of A part of wire = length of B part of wire = L, radius of A part of wire = r, radius of B part of wire = 2 r, number of antinodes in part A = p, number of antinodes in part B = q, the joint of two wires is a node. To find : p : q Mass per unit length of part A : ρπr 2 L µA = ...(i) L





(r is density of wire A = density of wire B) Mass per unit length of part B : ρπ(2r )2 L µB = = 4µ A ...(ii) L Speed of wave in part A : T vA = µA Speed of wave in part B : Τ 1 T = = vB µΒ 2 µA

...(iii)

...(iv)

160

Oswaal JEE (Main) Mock Test 15 Sample Question Papers Since, frequency of wave in wire A = frequency of wave in wire B. pv A p T ...(v) = fA = 2L 2L µ A = fB



pvB q T = 2L 4L µ A

...(vi)

21. (2) Given : Number of turns in a coil is N, radius of the coil is r, current through the coil is I, the coil is located in the XZ plane in a magnetic field Bi^. To find : t, the torque acting on the coil. Torque acting on the coil : τ = m× B (m = NIA is the magnetic moment of the coil) τ = NIAB sin 90 = NIAB= NIπr 2 B (A = p r2 is area of cross section of coil)

22. (1) Given : de-Broglie wavelength of particle 1 is l1, de-Broglie wavelength of particle 2 is l2, the two particles are moving at right angle to each other, the particles suffer a perfectly inelastic collision. To find: The de-Broglie wavelength l of the final particle. Momentum of particle-1 :







h λ1

Momentum of particle-2 : h p2 = λ2 Total momentum of the two particle system before collision : p=

p12 + p22 + 2 p1 p2 cos 90°

...(i)

As the collision is inelastic the two particles stick together and move as one after collision. By law of conservation of linear momentum, the momentum of final particle after collision will be :

 

p=

p12 + p22 + 2 p1 p2 cos 90 °

2

p=

 

 1   1  h = h   +  λ  λ1   λ 2  2

Equating equations (v) and (vi), p q T T = 2L µ A 4L µ A

p1 =



2

 h   h   h  h   +   + 2   λ1   λ 2   λ1   λ 2

 1   1  1 =   +  λ  λ1   λ 2    1 1 1 = + 2 2 2 λ λ1 λ 2

p:q = 1:2



2

=

  cos 90 ° 

2

2

23. (3) Given : The ratio of amplitudes of two interfering waves is a1 1 = (i) a2 3





Imax ,  the ratio of maximum Imin and minimum intensities of fringes in the interference pattern. Let intensity corresponding to amplitude a1 be I1 and intensity corresponding to amplitude a2 be I2. Then the ratio of maximum to minimum intensity in the interference pattern will be : To find :

2 I + I +  2 I1 I 2 Imax ( I1   + I 2 )  1 2 = = 2 Imin ( I1 − I 2 ) I1 + I 2 −  2 I1 I 2 As the intensity is directly proportional to 2 square of amplitude, putting = I1 a= I 2  a22 . 1 ,  

Imax a1 2 + a22 +  2 a1 a2 =  Imin a1 2 + a22 −  2 a1 a2 Now, putting a2 = 3a1, Imax 16 a1 2 4 = = = 4 :1 Imin 1 4 a1 2 24. (4) Given : R = 200 W. To find : New value of resistance R′, if in the colour code of R the red colour is replaced by green. For R = 200 = 20× 101 W, the colour code of the given resistor will be : 2 = Red,  0 = Black, 101 = Brown.

New colour code is : Green, black and brown. Green = 5, Black = 0, Brown = 101 The new colour code will correspond to : 1 ′ R = 50 × 10 = 500 Ω

161

Solved Paper-2019 25. (2) Given : Velocity of ship A,  vA = (30 ˆi + 50j ) km/h, Velocity of ship B  v = –10 ˆi km/h



Balancing the forces in equilibrium position of bob : T cos q = mg; T sin q = qE That gives, qE tan q = mg

B



Distance between two ships    = r – r = 80 ˆi + 150 j . B

A

To find : The time at which the distance between the two ships is minimum.   Let r A = 0 ˆi + 0 j ; that gives :   i + 150 j r = 80 ˆ

B



After time t :  i + 50t ; r A = 30t ˆ As ship B is moving towards west :   i + 150 j r B = (80 – 10t) ˆ

Distance between two ships after time t :   d = r B – r A  = (80 – 10t – 30t) ˆi + (150 – 50t) j

d2 = (80 – 40t)2 + (150 – 50t)2 For t to be the time when distance between the two ships is minimum : d 2 (d ) = 0 dt d [(80 – 40 t)2 + (150 – 50 t)2] = 0 dt



2(80 – 40 t)(– 40) + 2(150 – 50 t)(–50) = 0 –3200 + 1600 t – 7500 + 2500 t = 0; 107 ; t= 41 t = 2.6 26. (4) Given : Mass of bob of simple pendulum = 2g = 2 × 10–3 kg, Charge on bob = 5.0 mC = 5.0 × 10–6 C, Intensity of applied electric field = 2000 V/m. To find : Angle the pendulum makes with the vertical, q. y

x



T

T cos  

E qE

T sin  mg

 qE  5.0 × 10 −6 × 2000 q = tan −1  = 2 × 10 −3 × 10  mg  = tan–1 (0.5). 27. (3) Given : Radius of steel wire is r = 2.0 mm = 0.002 m, load on steel wire is m = 4 kg, m acceleration due to gravity is g = 3.1 p 2 . s To find : Tensile stress in wire. Force mg Tensile stress = = 2 Area πr 4 × 3.1π = π× 0.002 × 0.002

= 3.1 × 106 N/m2

28. (1) Given : Number of gas molecules is n = 1022, mass of each molecule is m = 10–26 kg, area of the surface over which the gas molecules are colliding elastically per second is A = 1 m2, speed of gas molecules is

v = 10 4 m/s

To find : Order of pressure exerted by the gas molecules on the surface. Change in momentum of a gas molecule colliding elastically with the surface is : ∆p= mv − ( −mv= ) 2 mv Change in momentum of n gas molecules colliding elastically with the surface is : ) 2nmv …(i) ∆p= mv − ( −mv= Force exerted by n gas molecules on the surface : ∆p 2nmv = F = = 2nmv  …(ii) 1 ∆t  (Dt = 1 s) Pressure exerted by n gas molecules on the surface: F 2mnv P = = A A 2 × 10 −26 × 10 22 × 10 4 = = 2   1 So, order of pressure exerted by gas molecules on the surface is 0.

162

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

29. (4) Given : Incident radiation is from transition ni = 2 to nf = 1 of hydrogen atoms, the radiation is incident on He+ ions, He+ ions are in states n = 1 and n = 2. To find : the possible transition of He+ ions. Energy of radiation coming from hydrogen atoms (Z = 1) :  1 1  E 13.6 (Z)2  2 − 2  eV =  n f ni    1 1 13.6  − = e  10.2 V 1 4 Energy levels of electron in He+ (Z = 2) ion : 13.6 (Z 2 ) En = n2 E1 =  −54.4 eV, E 2 =  −13.6 eV,  = E



E3 =  −6.04 eV, E 4 =  −3.4 eV



We can see : E 2 − E 4 ≈ E.  So, a photon of energy E = 10.2 eV will cause a transition n = 2 → n = 4 in a He+ ion.

30. (2) Given : Radius of pipe is r = 5 cm, rate of flow of water coming out of the pipe is V litres 100 litres = 100 , = t minute 60 second density of water is kg r = 1000 3 , m coefficient of viscosity of water is h = 1 mPa s. To find : Order of magnitude of Reynolds number for the flow. Reynolds number for flow of a liquid : ρ vD Re = η V ( v = t is velocity of flow, A is area of cross A section of pipe and D = 2r is diameter of pipe.) 2ρVr Re = tAη =

2ρVr tπr 2 η

=

2ρV r πtη

=

2 × 1000 × 100 × 10 −3 = 2 × 104 −3 0.05 × 3.14 × 60 × 1 × 10

Chemistry 31. (3) Ozone layer is depleted due to release of throw carbons (CFCs) UV C F2 Cl(g)  → Cl(g) + F2 Cl (g)

 Cl +O3 → ClO(g)+O 2 (g)

 ClO+O(g) → Cl + O2 Due to depletion of ozone layer the amount of uv radiation reaching the earth. This both statements are correct but reason in not the correct explanation of the assertion.

32. (1) According to Freundlich adsorption isotherm x = Kp 1 / n m

Taking logarithm on both sides we get x 1 log = log K + log p m n Comparing equation for straight line we get,

33. (3)

= y mx + C Slope ( m) =

1 n

1 value lies between 0 and 1 n 1 2 It is only possible when = n 3 Insoluble Insoluble Soluble Insoluble

m – cresol on reaction with 10%. NaOH gives 3-methyl sodium phenoxide. It is very weak acidic in nature i.e. way insoluble in 5% HCl or water and unable to give effervescence with 10%. NaHCO3. Salt is not formed with 10% NaHCO3.

163

Solved Paper-2019 Charge Size Li+ > Na+ > K+ > Rb+ > Cs+ L → R charge = const. size ↓ \ HE↓ 34. (3) H.E ∝

35. (2) The neutral molecules or ions (usually anions) which donates lone pair of electron to the central atom/ion is called ligand. In the example there are two anion parts and two neutral parts. Therefore the compound acts as a tetra dentate ligand. 36. (4) Maltose on treatment with dilute HCl gives D – glucose. Because it is composed of two a – D glucose formed by an a – glycosidic linkage between C1 of one unit and C4 of the other unit.



[Here CP =(23 + 0.01 T)] 1000



 0.01 T 2  3  23T + =  2  300 



3 =





 2 × 23 × 700 + 9100   2  

= 61950 J/mol = 62 kJ/mol

42. (4) For ideal solution, Ptotal = PA° × A + PB° × B \ Ptotal = {400 × 0.5 + 600 (1 – 0.5)} mm Hg = (200 + 300)mm Hg = 500 mm Hg Therefore mole fraction of A in vapour phase PA P° ×A = A YA = P P total

total

0.5 × 400 = 0.4 = 500





Mole fraction of B in vapour phase, YA + YB = 1 ⇒ YB = 1 – YA ⇒ YB = 1 – 0.4 ⇒ YB = 0.6

37. (4) From Ellingham diagram we can select the proper reducing agent like C(s) or Cu or Al for compound. 38. (3) As SRP ∝ oxidizing property. Here E°S O2− / SO is highest, therefore it acts as 2

8

4

strongest oxidizing agent. 39. (4) Neutral FeCl3 station reacts with phenolic— OH group active—CHO group containing aromatic aldehydes reduces by Fehling solution the compound which contains either keto methyl on oxidizes keto methyl group gives +ve iodoform test. Therefore option (d) is correct moreover if reacts with Grignard's reagent.

43. (2) The use of plastic bags in hazardous to our environment. 4+ 3– 44. (2) For Zr3(PO4)4  3Zr + 4PO4 SM  3 SM 4 SM 4+ 3 \ Ksp = [Zr ] [PO43–]4 ⇒ Ksp = (3 S)3 × (4 S)4 ⇒ Ksp = 27 × 256 × S7 1



 K sp  7 ⇒ S =    6912  This is the relation between molar solubility and solubility product.

45. (2) OCH3

40. (3) B2H6 + O2 → B2O3 + H2O B2H6 + H2O → H3BO3 + H2

–

H HBr

  DH =

∫ nCpdT

T1

Br

CH=CH2

+CH—CH3

T2

41. (1)

OCH3

OCH3 +

CH—CH3 Br OH

+

H

O —CH3 | H

+

HBr

Br – SN 2

+ CH3Br

1000



∫

n (23 + 0.01 T) dT = 300

CH—CH3

CH—CH3

Br

Br

164

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Z 1 46. (4) For any atom or ion   ∝ where Z = e r atomic or nuclear charge e = nuclear of electron and r = radius of atom or ion. Z Since varies inversely with ionic radius. C Z decrease in magnitude results in an e increase in ionic radius. Z 17 [For Cl–; = e 18 Z 18  Ar, = e 18 Z 20 Ca2+ = e 18 So, the order is [Cl– > Ar > Ca2+]

From 1st value we get, 0.045=K[0.05]m [0.05]n 



From 2 values we get, 0.090=K[0.10]m [0.05]n 

From 3rd value we get, 0.720=K[0.20]m [0.10]n ...(iii)



On dividing equation (ii) by (i) we get, 0.090  0.10  = 0.045  0.05 

2



2

4 3

4

2



m

51. (2) In presence of strong field ligands D0 > p, therefore electronic configuration becomes 2g4 eg0 giving low spin complexes. All the given complexes have strong field ligands CN– and NH3 respectively. Therefore they forms only low spin complexes as shown below. Complex

FeSO4 +MnO-4 → Mn 2++CO2 +Fe3+  ... (iii)

+

–

N2Cl

OH +

OH Base

N— —N

50. (1) Let the rate equation for the given reaction is, rate=K[A]m [B]n

Oxidation Configura- Orbital No. of state tion splitting unpaired electrons

4–

V2+

t2g3 eg0

3

[Fe(CN)6]4–

Fe2+

t2g6 eg0

0

[Ru(NH3)6]3+

Ru3+

t2g5 eg0

1

[Cr(NH3)4]2+

Cr3+

t2g4 eg0

2

[V(CN)6]



49. (1)

n

0.720  2   10  =   ×    0.090  1   5  ⇒ 8 = 2 × 2n ⇒ 2n = 4 ⇒ 2n = 2 2  n = 2 Therefore the rate law for the reaction is  Rate = K[A][B]2

... (ii)

Change in oxidation number of Mn is 5. Total change in oxidation in the above (i), (ii), (iii) equations are +3, +6, +1 respectively. \ No. of equivalent KMnO4  = Total change in oxidation numbers ⇒ n × 5 = 1 × 3 + 1 × 6 + 1 × 1 ⇒ n=2

m

m ⇒  2 = 2 m 1 ⇒  2 = 2 ∴   m = 1 ... (iv) On dividing equation (iii) by (ii) we get





... (ii)



47.(4) This reaction is a Friedel Craft's reaction.

48. (1) The oxidation of a mixture of one mole of each of FeC2O4, Fe2(C2O4)3, FeSO4 and Fe2(SO4)3 with KMnO4 in acidic medium is as follows. FeC 2 O4 +MnO4- → Mn 2++CO2 +Fe3+  ... (i) Fe (C O ) +MnO- → Mn 2++CO +Fe3+

... (i)

nd



Therefore the correct order of the spin only magnetic moment of metal ions which forms low spin complexes as follows V2+ > Cr2+ > Ru3+ > Fe

52. (2) The colour of Lanthanides elements depends in the number of unpaired electron present in the 4f orbital. Electronic

165

Solved Paper-2019

53. (4) Molecular weight of calcium bicarbonate = 162 Molecular weight of magnesium bicarbonate = 146 Molecular weight of calcium carbonate = 100 162 g of Ca(HCO3)2 = 100 g CaCO3 100 ×0.81 g CaCO3 162 = 0.5 g CaCO3 146 g of Mg(HCO3)2 = 100 g of CaCO3

0.81 g of Ca(HCO3)2 =



100×0.73 g of CaCO3 0.73 g of Mg (HCO3)2 = 146

= 0.5 g CaCO3 100 ml of sample water contains (0.5 + 0.5) g = 1 g of CaCO3 Thus hardness of water sample = 1 × 10 100 = 10,000 ppm

54. (3) According to selection rule, smaller the value of (n + l), lower is the energy level or between the two subshell having same value of (n + l), the subshell which have lower value of n will be lower level.



n

l

n+l

I

4

2

4+2=6

II

3

2

3+2=5

III

4

1

4+1=5

IV

3

1

3+1=1

Therefore the correct order of their increasing energies will be IV < II < III < I

55. (4) O

:

configuration of the green Lanthanides are as follows Gd3+ = 4f 7 Sm3+ = 4f  5 La3+ = 4f 0 Lu3+ = 4f 14 The ion which have full filled to orbital or absence of electron in f orbital will not give any colour. Gd3+ have half filled 4 f orbital which is stable configuration. Only Sm3+ have partly filled 4 f orbital which can easily undergoes excitation and results in the formation of colour.

O

O Br

CH

Br

NaBH4 MeOH

CH2

–BrO

56. (3) –

–

57. (2) No. of lattice points = No. of O2 voids \ No. of atoms of B = 4 1 No. of atoms of A = × No. of O2 voids 2 1 = ×4=2 2 No. of ‘O’ atoms = No. of all Td voids = 8 =A:B:O=2:4:8=1:2:4 The formula of the compound is AB2O4. 58. (3) Basic strength in aqueous solution (C2H5)2NH > C2H5NH2 > NH3 Considering +I effect and stability of conjugate acid in aqueous medium due to hydrogen bonding. 59. (2) 1st law of thermodynamics we get, DU= q + W For cyclic process DU = O; q = –W (a) is correct For adiabatic process q = 0 DU = W (b) is incorrect For isochoric process; DV = 0 Again W = PDV \ W = 0 \ DU = q (c) is correct For isothermal process, D = 0 \ q = –W (d) is correct 60. (1) Only primary amine can be prepared by Gabriel Phthalimide reaction with better SN2. O C KOH NH –H2O C O O C OH C OH O

O C CH3CH2CH2X NK C O

+CH3CH2CH2NH2

H 3O+

O C N — CH2CH2CH3 C O

166

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Mathematics 61. (2)

(x +

x -1 3

) + (x 6

x -1 3

)



= 6 C 0 x 6 + 6 C1 x 5 x 3 - 1 + 6 C 2 x 4

(

x3 - 1

)

on curve

2

) + C x - C x x -1 + C x ( x - 1 ) .... + C ( x - 1 ) æ ö = 2 ç C + C x ( x - 1 ) + ... + C ( x - 1 ) ÷ è ø +... + C 6 6

(

x -1 3

6

4

6

6

6

6

5

0

6

6

6

0



6

4

3

2

6

6

3

2

6

= 2{ 6 C 0 + 6 C 2 x 4 ( x 3 - 1)1 + 6 C 4 x 2 ( x 3 - 1)2 + 6 C 6 ( x 3 - 1)3





7 4 distance between line and curve x-y =



7 4

Sum of even power 2( 6 C 0 - 6 C 2 + 6 C 4 + 6 C 4 - 6 C 6 ´ 3 - 6 C 6 )



7 -0 7 4 = 1+1 4 2

= 24

64. (1)

6

4

3

6

2

6

3

+ 6 C 6 ( x 9 - 3x 6 + 3x 3 - 1)



1 9ö æ = 1ç x - ÷ 2 4ø è

x–y=

= 2{ C 0 + C 2 x ( x - 1) + C 4 x ( x - 2 x + 1)

62. (1) cos  =

3 5

tan  =

5

4

10





sin( a - b) = sin a cos b - cos a sin b

4 3 3 1 = ´ - ´ 5 5 10 10 9 sin( a - b) = 5 10 æ 9 ö Þ a - b = sin -1 ç è 5 10 ÷ø 63. (3) y = x line and curve y2 = x – 2 tangent parallel to y2 = x – 2 & line y = x dy dy = 1, =1 2y dx dx



æaö ç ÷ èbø

3



a = 1 + i, b = 1 - i

Let

1

 3

x 2 - 2x + 2 = 0 2± 4-8 x = 2 x = 1±i



1 3





tangent, y -

9 4



6



x=

⇒

6

3

2





y2 = x – 2

1

2

3

3

1 2

y=

6



æ1+i ö ç 1-i ÷ è ø

Þ

n

= 1

n

= 1

n

Þ

ì (1 + i )2 ü í ý = 1 (by rationalization) î (1 + i )(1 - i ) þ in = 1

Þ Least x is 4. 65. (3)

A Ì B Þ P(A Ç B) = P(A) P(A Ç B) æ Aö Pç ÷ = è Bø P(B)

66. (4)

dy 1 = dx 2 y



1 =1 2y



æ Aö = P ç ÷ ³ P(A) è Bø

2 + 4 + 10 + 12 + 14 + x + y = 8 7 x + y = 14 ...(i) 2 2 + 4 2 + 10 2 + 12 2 + x 2 + y 2 - 8 2 = 16 7 x 2 + y 2 = 560 - 460

167

Solved Paper-2019 x 2 + y 2 = 100 …(ii) ( x + y )2 = 14 2



Þ

x 2 + y 2 + 2 xy = 196 Þ Þ

2 xy = 96, xy = 48

67. (1)

f ( x ) = log(1 - x ) - log(1 + x ) æ 2x fç 2 è1+ x

2x ö æ ÷ = log ç 1 2 ø è 1+ x

= log



(1 - x ) (1 + x ) - log 2 1+ x 1 + x2 2

æ1-x ö = log ç ÷ è1+ x ø 1-x = 2 log 1+ x = 2 f (x)



2

2

68. (1) f(x) = 9x4 + 12x3 – 36x2 + 25 f'(x) = 36x3 + 36x2 – 72x = 36x(x2 + x – 2) = 36x(x + 2) (x – 2) f'(x) = 0 for maximum and minimum 36x(x + 2)(x – 1) = 0 x = 0, 1, –2 f"(x) = 108x2 + 72x – 72 = 36(3x2 + 2x – 2) f"(0) = –2    then maximum if f"(c) is –ve then maximum f '(1) = +ve    Minimum at x = 1 f"(0) is +ve then mimimum f"(– 2) =+ ve so Minimum dy + 2 x( x 2 + 1) y = 1 69. (3) ( x + 1) dx dy 2 xy 1 + 2 = 2 dx x + 1 ( x + 1)2 2



2

From linear differential equation 2x 1 P = 2 Q= 2 x +1 ( x + 1)2 2x / x y eò

2

+ 1 dx

y e log( x

2

+ 1)

2 x / x 2 + 1 dx 1 = ò 2 eò dx + C 2 ( x + 1)

=



y( x 2 + 1) =

2 1 e log( x +1) dx + C 2 + 1)

ò (x

2

òx

1 dx + C +1

2

y( x 2 + 1) = tan -1 ( x ) + C



Þ





C = 0 y( x + 1) = tan -1 x 2





2x ö ö æ ÷ - log ç 1 + 2 ÷ ø è 1+ x ø

y(0) = 0 (given)



p then a = ? 32 Put x = 1 ....(i) y(1){1 + 1} = tan -1 1 a y(1) =

p 8 Substituting in equation (i) p p a´ = 8 32 1 a = 16 y(1) =

70. (3)

P (h, k)

A (0, 1)

O (0, 0)

1 + ( h - 0)2 + ( k - 0)2 + ( h - 0)2 + ( k - 1)2 = 4



h 2 + ( k - 1)2 = 3 - h 2 + k 2 Squaring both the sides. h2 + k 2 - 2k + 1 = 9 + h2 + k 2 6 h2 + k 2



Þ

-2 k - 8 = -6 h 2 + k 2



Þ

k + 4 = 3 h2 + k 3

Squaring both the sides. k2 + 16 + 8k = 9h2 + 9k2



 

9h2 + 8k2 – 8k – 16 = 0

Thus 9x2 + 8y2 – 8y – 16 = 0

71. (3)  f(x) = f(x) + f(2 – x)

f'(x) = f'(x) – f'(2 – x)

for increasing and decreasing

f'(x) = 0 ⇒ f'(x) = f(2 – 2)  x = 2 – x  x = 1

interval



sign of f'(x) –ve +ve



So increasing in (1, 2) and decreasing in (0, 1)

Graph

(0, 1)

(1, 2)

168

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

f (x)

2 - 1 + cos x 'L' Hospital Rule 2 sin x cos x lim x ®0 1 ( - sin x ) 02 1 + cos x

72. (4)

2

1



écos a - sin a ù A = ê ú ë sin a cos a û

75. (4) Plane ^ to i + j + k and i + 2 j + 3k

écos a - sin a -2 cos a sin a ù = ê ú 2 2 ë 2 sin a cos a cos a - sin a û 2

Similarly,

Þ

73. (1)

cos 32a = 0 p 32a = , 2 p a = , 64 2

& sin 32a = 1 p 32a = 2 p a = 64

2

 4x + y = 8

Tangent at (1, 2), 4x.1 + y.2 = 8 2x + y = 4



...(i)

m1 = –2

Tangent at (a, b), 4xa + yb = 8 m2 =

...(ii)

æ -4a ö –2 ç ÷ = –1 è b ø – 8a = b...(iii)



= i - 2 j + k   Projection of 2i + 3j + k on i – 2j + k is 1+ 4 +1



=

76. (3) For non-trivial solution, 1 -c c -1 c c 2 2 1(1 - c ) + c( -c - c ) - c( c 2

3 2

D = 0 -c c = 0 -1 + c) = 0



1 - c - c - c - c - c2 = 0



1 - 3c 2 - 2 c 3 = 0



2 c 3 + 3c 2 - 1 = 0

2

2

3

3

By remainder theorem ( c + 1)2 (2 c - 1) = 0 c = -1,



Greatest value of c =

1 2

...(iv)

q ∫ you are citizen of India p ⇒ q Contrapositive ~q ⇒ ~p ∫ if you are not citizen of India then you are not born in India.

78. (4) (0, 3)

(h, h)

2

a2 = 17

1 2

77. (2) p ∫ you are born in India



64a2 = 8 – 4a2





m1m2 = –1

Eqn (iii) & (iv), 64a2 = b2

k

1 1 1 = i(3 - 2) - j(3 - 1) 1 2 3 + k (2 - 1)



–4a b

(a, b) lies on ellipse 4a2 + b2 = 8

j

(i - 2 j + k )(2i + 3 j + k )

écos 32a - sin 32a ù é0 -1ù A 32 = ê ú=ê ú ë sin 32a cos 32a û ë 1 0 û



i

2

écos 2a - sin 2a ù = ê ú ë sin 2a cos 2a û



= 4√2

écos a - sin a ù écos a - sin a ù A2 = ê úê ú ë sin a cos a û ë sin a cos a û



æ 0ö çè 0 ÷ø form

x®0

0

sin 2 x

74. (2) lim

(5, 0)

169

Solved Paper-2019

Line 3x + 5y = 15 Let the point (h, h) which are equidistant from coordinate axis 1st quadrant (h, h) 3h + 5h = 15 15 æ 15 15 ö Point ç , h = ÷ 8 è 8 8 ø

2nd quadrant (–h, h) –3h + 5h = 15 15 h = 2 æ -15 15 ö ç 2 , 2 ÷ satisfied è ø



2

1 3 + +8 3 2 2 + 9 + 48 59 sq. units = = 6 6 =



81. (1) 1, 1, 2, 2, 2, 2, 3, 4, 4, Odd digit in even place ¯

y = x 2 + 3x 3ö 9 æ = çx + ÷ 2ø 4 è 3

 x - y - z = 0



¯

¯

4 Even places and 2, 2, 2, 2, 4, 4 6 numbers which are even so 1, 1, 3 only 3 odd places 3! that can be placed in 4 Even places 4 C3 ´ 2! for even place.



Remaining Even numbers in 6 places by



9

Parabola with vertex æç - , - ö÷ passing 4ø è 2 origin

¯



2



1

é x 3 3x 2 ù x x dx ( 3 ) 4 2 + + ´ = ê + ú +8 ò0 2 û0 ë3 1

(2 x - y - 4) + l( y + 2 z - 4) = 0 80. (4) Passes (1, 1, 0) ⇒ l = -1 Plane (2 x y 4) ( y + 2 z - 4) = 0

4th quadrant (h, – h) 3h – 5h = 15 -15 h = 2 æ -15 15 ö ç 2 , 2 ÷ satisfied è ø



x = -4, 1





3rd quadrant (–h, –h) – 3h – 5h = 15 -15 h = 8 æ 15 15 ö Point ç , ÷ not satisfied è 8 8 ø

79. (2)

( x + 4)( x - 1) = 0





6! 4 !2!

So total ways 3! 61 ´ ´ = 180 2! 4 !2!

82. (4)

2, A. (

–1,

4)

(–3,

 −3 −9  0 £ x £ 3  ,  0 £ y £ 4 2 4 Required area OABC this can be divided into OCD + Rectangle DABC Area OCD For C point solve y = 4 & y = x2 + 3x

x 2 + 3x = 4



x 2 + 3x - 4 = 0

+2,

0)

B D'r



,1 , –7

10

From (2, –1, 4) Any point of the line y-2 z x+3 = = =l 10 -7 1 x = 10l - 3, y = -7 l + 2, z = l

AB & line are ^ D'r of AB 10l –3 –2, –7l + 2 + 1, l – 4 10(10l - 5) + ( -7)( -7 l + 3) + 1( l - 4) = 0

170

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

l =



1 2



1 1 æ ö æ ö 1 Point ç 10 ´ - 3 ÷ , ç -7 ´ + 2 ÷ , 2 2 è ø è ø 2 æ -3 1 ö , = ç 2, 2 2 ÷ø è



1ö æ3 ö æ Distance = (2 - 2) + ç + 1 ÷ + ç 4 - ÷ » 3.57 2 2ø è ø è



2

2

2



x < 2 Þ 2- x +x-4 x +2 = 0

(i) For

x - 5 x + 4 = 0

(



⇒

∴ 85. (3)

x-4

)(

)

x - 1 = 0 Þ x = 1| x = 16

x = 1 is solution

Sum of solution = 1 + 9 = 10 cos(α

3 5

β)

sin(α

β)

5 13

83. (4) 5

(0, 0) O

A

12

n2 2 n2 AC = 2AB = 2 16 2 = 2 16 -



n = 2

æ 12 ö AC = 4 ç 16 - ÷ = 62 2ø è æ 22 ö AC2 = 4 ç 16 - ÷ = 56 2 ø è

=

86. (2) 2. 20 C 0 + 5. 20 C1 + 8. 20 C 2 + ... + 62. 20 C 20 20





84. (3) | x - 2| + x ( x - 4) + 2 = 0



(i) For

x ³ 2 Þ x -2 +x-4 x +2 = 0



x -3 x = 0 x

(

)

x -3 = 0

x = 0|x = 9 ⇒ x = 9 is solution

r =0



æ 5 ö n = 2 AC2 = 4 ç 16 - ÷ = 14 2 ø è Sum 210 2



å (3r + 2)

2



n = 4

tan( a + b) + tan( a - b) 1 - tan( a + b)tan( a - b)

4 5 + = 3 12 4 5 1- ´ 3 12 63 = 16



æ 32 ö AC2 = 4 ç 16 - ÷ = 46 2 ø è æ 42 ö AC2 = 4 ç 16 - ÷ = 62 2 ø è

n = 3

tan 2a = tan[( a + b) + ( a - b)]



Circle x2 + y2 = 16 O (0, 0), r = 4 chord x + y = n | 0 + 0 - n | +n = OB = 1+1 2 AC = 2AB = 2 OA 2 - OB 2

n = 1

α−β

C

B

5

13

α+β 3

AC = 2



4

20

å 3r

Þ

r =0

Þ

20

20

r =0 20

år r =0

20

Cr + 2å r =0

20

æ 2, 5, 8 ... A.P. ö Cr ç ÷ è 2 + ( n - 1)3 ø

Cr

3 ´ 20 ´ 219 + 2 ´ 2 20 = 219 (60 + 4)

Þ where,

å

20

20

= 219 ´ 2 6 = 2 25

C r = Sum of binomial coeff. = 2 20

20

C r = write (1+ x )20 expansion, then differenciate & substitute x = 1

87. (3) 91 = 13 × 7 \ HCF (91, n) > 1 sum of n = multiple of 7 + multiple of 13 – multiple of 13 × 7 = (105 + .......+ 196) + (104+ .......195) –182 = 7(105+196) + 4 (104 + 195) – 182 = 2107 + 1196 – 182 = 3121

171

Solved Paper-2019

ò

88. (3)

ò

5x 2 dx x sin 2

sin

90. (3)

5x x cos 2 2 dx x x 2 sin cos 2 2



3 sin x - 4 sin 3 x + 2 sin x cos x dx ò sin x

=

ò (3 - 4 sin

=

æ ö æ 1 - cos 2 x ö + 2 cos x ÷ dx ç3 - 4ç ÷ 2 è ø è ø

= =

3x + 2 sin x - 2 x + sin 2 x + C x + 2 sin x + sin 2 x + C

ò

p/4

ò

p/4

-p / 4

-p / 4

2

x + 2 cos x ) dx

2



æ æp öö = ç cot -1 tan ç + x ÷ ÷ è3 øø   è



æp æp öö = ç - tan -1 tan ç + x ÷ ÷ 2 3 è øø   è

g ( x ) = log e x h( x > 0)

2 - x cos x 2 + x cos x 2 + x cos x h( -x ) = log e 2 - x cos x h( x ) = log e

Let

æ 2 - x cos x ö = log e ç ÷ è 2 + x cos x ø



p/4

-p / 4

h( x ) = 0 = log e 1

2 ìæp ö ï ç -x÷ ïè6 ø 2y = í 2 ö ïæ 7 p x ÷ ïç 6 ø îè  

0 CH3CH2Cl > (CH3)3CCl (4) CH3Cl > CH3CH2Cl > (CH3)2CHCl > (CH3)3CCl Q. 43. The major product of the following reaction is:

Q. 45. Among the following statements on the nitration of aromatic compounds, the false one is : (1) The rate of nitration of benzene is almost the same as that of hexadeuterobenzene (2) The rate of nitration of toluene is greater than that of benzene (3) The rate of nitration of benzene is greater than that of hexadeuterobenzene (4) Nitration is an electrophilic substitution reaction Q. 46. To prepare 3-ethylpentane-3-ol, the reactants needed are : (1) CH3CH2MgBr + CH3COCH2CH3 (2) CH3MgBr + CH3CH2CH2COCH2CH3 (3) CH3CH2MgBr + CH3CH2COCH2CH3 (4) CH3CH2CH2MgBr + CH3COCH2CH3 Q. 47. In a set of reactions nitrobenzene gave a product D. Identify the product D.

(1)

(1)







(3) (4)







Q. 44. Major product of the reaction is : HCl (1 eq.)

(1)



(2)

Cl

(3)



Cl





(4)

Q. 48. Give the order of decarboxylation of the following acid : CH3COOH; CH2 =CH–CH2 – COOH ; I II NO2

(2)

(3)

(2)

Cl (4)

Cl

CH2(COOH)2 ; O2N

COOH

NO2 III IV (1) I > II > III > IV (2) III > IV > II > I (3) IV > III > II > I (4) I > III > II > IV Q. 49. The major product of the following reaction is:

177

Mock Test PaPER-1

(1)



(2)





degree. The heat of reaction for the change taking place inside the cell is ............ kJ/mole. Q. 53. The energy released in joule and MeV in the following nuclear reaction

N=N

2 1



2 Assume that the masses of 1 H , 32 He and neutron (n) respectively are 2.0141, 3.0160 and 1.0087 in amu, is .......... × 10–13 J. A unit cell of sodium chloride has four formula units. The edge length of the unit cell is 0.564 nm. The density of sodium chloride is ................ g/cm3. If weight of the non-volatile solute urea (NH2—CO—NH2) to be dissolved in 100 g of water, in order to decrease the vapourpressure of water by 25%, then the weight of the solute will be ................ g. Volume of N2 at NTP required to form a monolayer on the surface of iron catalyst is 8.15 ml/g of the adsorbent. The surface area of the 100 g adsorbent if each nitrogen molecule occupies 16 × 10–22 m2 will be ................ m2. The number of p-bonds are present in marshall's acid is ......... . The effective atomic number (EAN) of a metal carbonyl, m(Co)x is 36. The atomic number of the metal is 26. The value of 'x' is .......... . The magnetic moment of central atom of [Co(NH3)6]3+ is …….. Au + CN– + H2O + O2 → [Au(CN)2]– + OH–. The number of CN– ions are involved in the balanced equation is .......... .

N=N

Q. 54.

(3) Q. 55.

(4) Q. 56.

Q. 50. The number of asymmetric carbon atom in the glucose molecule in open and cyclic form is: (1) Four, Five (2) Four, Four (3) Five, Four (4) Five, six

Q. 57.

Section B Q. 51. The specific rate constant of the decomposition of N2O5 is 0.008 min-1. The volume of O2 collected after 20 minutes is 16 ml. The volume that would be collected at the end of reaction. NO2 formed is dissolved in CCl4 ............... ml. Q. 52. The e.m.f. of cell Zn | ZnSO4 || CuSO4| Cu at 25°C is 0.03 V and the temperature coefficient of e.m.f. is –1.4 × 10–4 V per

H +12 H ®32 He +10 n



Q. 58.

Q. 59. Q. 60.

Mathematics Section A Q. 61. The statement ∼ (p ↔ ∼ q) is: (1) a tautology (2) a fallacy (3) equivalent to p ↔ q (4) equivalent to ∼ p ↔ q

tan 2q + tan q = 0, then the general value 1 - tan q tan 2q of q is :

Q. 62. If

np ;n∈I 3 (4) np ; n ∈ I (3) np ; n ∈ I 4 6 Q. 63. The mean of a data set consisting of 20 observations is 40. If one observation 53 was wrongly recorded as 33, then the correct mean will be :

(1) np ; n ∈ I

(2)

(1) 41

(2) 49

(3) 40.5

(4) 42.5

178

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 64. In a triangle ABC, in usual notation, (a + b + c) (b + c – a) = lbc will be true if : (1) l < 0 (2) l > 0 (3) 0 < l < 4 (4) l > 4 Q. 65. In an equilateral triangle of side 2 3 cm, the circum radius is : (1) 1 cm (2) cm (3) 2 cm (4) 2 3 cm

ì 1 if x is rational Q. 73. If f(x) = í-1 if x is irrational is continuous î

on : (1) R (3) (–1, 1)

p p p

............. p p ­____________­ n radical signs where p ≥ 2, p ∈ N ; n ∈ N when simplified is : (1) independent of p

(2) independent of p and of n (3) dependent on both p and n (4) positive Q. 67. The number of real solutions of the equation x

æ 9 ö = –3 + x – x2 is: ç 10 ÷ è ø (1) 1 (2) 2 (3) 0 (4) 3

(2) 75

(3) 750

(4) 900

Q. 69. The middle term in the expansion of (1–3x + 3x2 – x3)6 is : (3) 18C9 x9 m+n

Q. 70. If P2 = 90 and given by :

(2)

18

C9 (–x)9

(4)

18

C9 x10

m–n

P2 = 30, then (m, n) is

(1) (7, 3)

(2) (16, 8)

(3) (9, 2)

(4) (8, 2)

Q. 71. The domain of function is f(x) = (1) (1, 4) (3) (2, 4)

- log 0.3 ( x - 1) x 2 + 2x + 8

1 - cos 2 x is: Q. 72. lim x ®0 2x (1) 1 (3) zero

x

+ 2y

x

y

-2

) )

is:

(2) (–2, 4) (4) (2, ∞)

( ( (2

Q. 76.

ò

(a

x

- bx

ax b x

)

2

dx equals :

(3) æç a ö÷ èbø p/4

Q. 77.

ò 0

x

x

b (2) æç ö÷ + 2x + c èaø x

– 2x + c

b (4) æç ö÷ – 2x + c èaø

sec 2 x dx equals : (1 + tan x )( 2 + tan x )

2 (2) loge 3 3 1 4 4 (3) log e (4) log e 2 3 3 p p 2 Q. 78. Area bounded by y = sec x, x = , x = 6 3 and x- axis is : 2 3 (2) (1) 3 2 (1) loge

2 2 (4) 3 3 Q. 79. The solution of the differential equation dy –1 = 0, is (1 + y2) + (x – etan y) dx –1 –1 (1) xe2tan y = etan –1y + k (2) (x – 2)–1= ke2tan –1y (3) 2xetan y = e2tan y + k –1 –1 (4) xetan y = tan y + k Q. 80. The smallest positive integer n for which

(3)

n

(2) –1 (4) does not exist

) )

x+y - 2x ) 2y - 1 (3) 2 · (4) 1 - 2x 2y Q. 75. If m be the slope of a tangent to the curve e2y = 1 + 4x2, then : (1) m < 1 (2) |m| ≤ 1 (3) |m| > 1 (4) |m| ≥ 1

x–y

x

(1) 909

(1) 18C10 x10

(2 (2

(1) æç a ö÷ + 2x + c èbø

Q. 68. If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to :

dy is equal to : dx 2x + 2y (2) 1 + 2x + y

Q. 74. If 2x + 2y = 2x+y, then (1)

Q. 66. The expression logp log p

(2) f (4) (–1, 0)

æ 1 + i ö = –1 is : ç 1-i ÷ è ø (1) 1 (3) 3

(2) 2 (4) 4

179

Mock Test PaPER-1 Section B Q. 81. Two boxes are containing 20 balls each and each ball is either black or white. The total number of black balls in the two boxes is different from the total number of white balls. One ball is drawn at random from each box and the probability that both are white is 0.21 and the probability that both 100 k is equal to .......... . are black is k, then 13 8 2 x x Q. 82. If x ∈ R 2 x 8 = 0 , then 2 x 8 2 to .......... . Q. 83. If

A

is

a

square

matrix

Q. 87. If two circles x 2 + y 2 + 2n1 x + 2 y +

1 = 0 and 2

1 , intersect each 2 other orthogonally where n1, n2 ∈ I, then number of possible of ordered pairs (n1, n2) is .......... . Q. 88. Let a variable point A be lying on the directrix of parabola y2 = 4 ax (a > 0). Tangents AB and AC are drawn to the curve where B and C are points of contact of tangents. The locus of centroid of DABC is a conic whose l length of latus rectum is l, then is equal a to ................ x 2 + y 2 + n2 x + n2 y + n1 =

is equal

such

that

é3 0 0 ù adj(adjA) is equal A(adjA) = êê0 3 0 úú , then adjA êë0 0 3 úû

to .......... .   Q. 84. If a = ( lx )ˆi + ( y )ˆj + (4 z )kˆ, b = yiˆ + xjˆ + 3 ykˆ ,  c = - ziˆ - 2 zjˆ - ( ( l + 1)x ) kˆ are sides of triangle as shown is figure then value of l is .......... . (where x, y, z are not all zero) b

c

 point Q of the line L such that PQ is parallel to the given plane are (a, b, g), then the product bg is .......... .  Q. 86. A rectangle PQRS has sides PQ = 11 and QR = 5. A triangle ABC has P as orthocentre, Q as circumcentre, R as mid point of BC and S as the foot of altitude from A. Then length of BC is k, where k/4 is equal to .......... .

a Q. 85. Consider a plane 2x + y – 3z = 5 and the point P(–1, 3, 2). A line L has the equation x - 2 y - 1 z - 3 . The co-ordinates of a = = 3 2 4

Q. 89. The ratio of the area of the ellipse and the area enclosed by the locus of mid-point of PS where P is any point on the ellipse and S is the focus of the ellipse, is equal to ................

x2 y2 Q. 90. If the radii of director circles of 2 + 2 = 1 a b x2 y2 and (a > b) are 2r and 1 = a2 b 2 2 e r respectively, then 22 is equal to (where e1 e1, e2 are their eccentricities respectively)

Answers Physics Q. No.

Answer

1 2 3 4 5 6 7 8 9

(2) (4) (4) (2) (3) (1) (2) (1) (4)

10

(1)

Topic Name

Q. No.

Answer

Topic Name

Kinematics Kinetic theory of gases One Dimension Projectile Motion Newton’s Laws Of Motion Friction Circular Motion Work Energy and Power Electromagnetic field

16 17 18 19 20 21 22 23 24

(2) (2) (2) (2) (1) 4.00 8.00 7.00 5.00

Equal potential surface Current Electricity Magnetic Effect of Current Ray Optics Atomic Structure & Matter Wave Nuclear Physics & Radioactivity Photoelectric Effect Refraction at Plane Surface Capacitance

Angular momentum

25

1.00

Electromagnetic Induction

180 11 12 13 14 15

Oswaal JEE (Main) Mock Test 15 Sample Question Papers (3) (3) (1) (2) (3)

Gravitation Simple harmonic motion Properties of Matter Fluid Mechanics Electrostatics

26 27 28 29 30

8.00 1375 140 1.00 300

Alternative Current Calorimetry Kinetic Theory of Gases Thermodynamics Sound Wave

Chemistry Q. No.

Answer

31

(4)

32 33 34

(1) (3) (3)

35 36 37

Topic Name

Q. No.

Answer

Topic Name

Mole Concepts

46

(3)

Alcohol, Ether, Phenol

Chemical Bonding Atomic Structure Electrochemistry

47 48 49

(1) (3) (2)

Nitrogen Compound Carboxylic Acid Nitrogen Containing

(4) (1) (4)

Gaseous State Chemical Energetics Redox Reaction

50 51 52

(1) 17.94 13.84

Biomolecules Chemical Kinetics Electrochemistry

38

(4)

Chemical Equilibrium

53

5.22

Nuclear Chemistry

39 40 41

(1) (4) (2)

Ionic Equilibrium Haloarens Alcohol

54 55 56

2.16 111.1 35.00

Solid State Solution Surface Chemistry

42

(2)

Haloalkanes

57

4.00

p-Blocks

43 44 45

(4) (3) (3)

Carbonyl Compound Halogen Derivative Aromatic Compound

58 59 60

5.00 0.00 8.00

Coordination Compound Coordination Compound Metallurgy

Mathematics Q. No.

Answer

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

(3) (2) (1) (3) (3) (1) (3) (4) (2) (4) (4) (4) (2) (3) (2)

Topic Name m. reasoning Trigonometric Equation Statistics Solutions of Triangle Properties of Triangles Logarithms Quadratic Equations Progressions Binomial Theorem Permutation and Combination Function Limit Continuity Differentiation Tangent & Normal

Q. No.

Answer

76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

(4) (4) (1) (3) (2) 2.00 5.00 9.00 0.00 6.00 7.00 2.00 3.00 4.00 4.00

Topic Name Indefinite Integration Definite Integration Area Under Curve Differential Equations Complex Number Probability Determinants Matrices Vectors Three Dimentional Geometry Straight Lines Circles Parabola Ellipse Hyperbola



2

MOCK TEST PAPER Time : 3 Hours

Total Marks : 300

General Instructions : 1. 2. 3.

4. 5. 6.

There are three subjects in the question paper consisting of Physics (Q. no. 1 to 30), Chemistry (Q. no. 31 to 60) and Mathematics (Q. no. 61 to 90). Each subject is divided into two sections. Section A consists of 20 multiple choice questions & Section B consists of 10 numerical value type questions. In Section B, candidates have to attempt any five questions out of 10. There will be only one correct choice in the given four choices in Section A. For each question 4 marks will be awarded for correct choice, 1 mark will be deducted for incorrect choice for Section A questions and zero mark will be awarded for not attempted question. For Section B questions, 4 marks will be awarded for correct answer and zero for unattempted and incorrect answer. Any textual, printed or written material, mobile phones, calculator etc. is not allowed for the students appearing for the test. All calculations / written work should be done in the rough sheet is provided with Question Paper.

Physics Section A    Q. 1. The magnitude of vectors A , B and   C are  respectively 12, 5 and 13 units   and A+B = C , then the angle between A and B is : (1)  0 (2) π π 2

π 4 Q. 2. A wave is represented by y = a sin (At – Bx + C) where A, B, C are constants and t is in seconds and x is in metre. The Dimensions of A, B, C are : (1) [T –1], [L], [M0L0T0] (2) [T –1], [L–1], [M0L0T0] (3) [T], [L], [M] (4) [T –1], [L–1], [M–1] Q. 3. A body moves in a straight line along, x-axis. Its distance x (in metre) from the origin is given by x = 8t – 3t2. The average speed in the interval t = 0 to t = 1 second is : (1) 5 ms–1 (2) – 4 ms–1 (3) 6 ms–1 (4) zero Q. 4. In a legend the hero-kid kicked a toy pig so that it is projected with a speed greater than that of its cry. If the weight of the toy pig is assumed to be 5 kg and the time of contact 0.01 sec., the force with which the hero-kid kicked him was (Speed of cry = 330 m/s) : (3)

(4)

(1) 5 × 10–2 N (2) 2 × 105 N (3) 1.65 × 105 N (4) 1.65 × 103 N Q. 5. A racing car is travelling along a track at a constant speed of 40 m/s. A T.V. camera man is recording the event from a distance of 30  m directly away from the track as shown in figure. In order to keep the car under view in the position shown, the angular speed with which the camera should be rotated, is : Track

car 40 m/s

30 m 30°



TV Camera

4 (1) rad/s 3 8 3 rad/s (3) 3

(2)

3 rad/s 4

(4) 1 rad/s

Q. 6. A pendulum of mass m and length  is suspended from the ceiling of a trolley which has a constant acceleration a in the horizontal direction as shown in figure. Work done by the tension is (In the frame of trolley) :

182

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

 a

m

mg –1 (1) [cos(tan ( a / g ) − 1] tan θ mg –1 (2) [sin(tan ( a / g ) − 1] tan θ mg (3) [sin(tan -1 ( a / g ) - 1] cos θ mg –1 –1 (4) [cos (tan ( a / g ) − 1] cos θ Q. 7. Figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting A and B do not slip on the wheels. If x and y be the distances travelled by A and B in the same time interval, then :

air is 340 m/s, find the frequency observed by a stationary observer. (i) if observer is in front of the source (ii) if observer is behind the train (1) 186 Hz, 216 Hz (2) 216 Hz, 186 Hz (3) 172 Hz, 220 Hz (4) 220 Hz, 172 Hz Q. 11. Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is 25. The intensities of the sources are in the ratio : (1) 25 : 1 (2) 5 : 1 (3) 9 : 4 (4) 625 : 1 Q. 12. A spherical surface of radius R separates two medium of refractive indices m1 and m2, as shown in figure. Where should an object be placed in the medium 1 so that a real image is formed in medium 2 at the same distance ? µ1

µ2 P

O

I

x

x

 µ 2 − µ1  (1)  µ + µ  R 2 1 A

B



(1) x = 2y (2) x = y (3) y = 2x (4) None of these Q. 8. The velocities of a particle in SHM at positions x1 and x2 are v1 and v2, respectively, its time period will be

(v (1) 2π (x (x (3) 2π (v

2 1

− v22

2 2

2 1

−x

2 1

− x 22

2 2

− v12

) )

) )

(2) 2π

(4) 2π

(x (v (x (v

) −v ) +x ) +v )

2 1

+ x 22

2 2

2 1

2 1 2 2

2 2

2 1

Q. 9. One cubic plate, having 15 cm side, floats on water surface. If surface tension of water is 60 dyne/cm. To lift this plate from water, Find the extra force required against weight. (1) 3600 dyne (2) 1800 dyne (3) 900 dyne (4) 7200 dyne Q. 10. A train moving at 25 m/s emits a whistle of frequency 200 Hz. If the speed of sound in

 µ + µ1  (3)  2 R  µ 2 



 µ 2 + µ1  R (2)   µ 2 − µ 1   µ2  R (4)   µ 2 + µ 1 

Q. 13. The dispersive powers of flint glass and crown glass are 0.053 and 0.034, respectively and their mean refractive indices are 1.68 and 1.53 for white light. Calculate the angle of the flint glass prism required to form an achromatic combination with a crown glass prism of refracting angle 4° : (1) 2° (2) 4° (3) 5° (4) 6° d = 10 −4 Q. 14. In young's double slit experiment D (d = distance between slits, D = distance of screen from the slits). At a point P on the screen resulting intensity is equal to the intensity due to individual slit l0. Then the distance of point P from the central maximum is (λ = 6000 Å) (1) 2 mm

(2) 1 mm

(3) 0.5 mm

(4) 4 mm

183

MOCK TEST PAPER-2 Q. 15. The mobility of electrons in a semiconductor chip of length 10 cm is observed to be 1000 cm2/Vs. When a potential difference of v is applied across it. What is the drift speed of electrons. (1) 1 cm/s

(2) 5 cm/s

(3) 2000 m/s

(4) 1000 m/s

Q. 16. The energy levels of a certain atom for first, second and third levels are E, 4E/3 and 2E, respectively. A photon of wavelength λ is emitted for a transition 3 → 1. What will be the wavelength of emission for transition 2 → 1 ? λ (1) 3

(2)

3λ (3) 4

(4) 3λ

Q. 17. The graph of ln 

R   R 0 

4λ 3

Section B

versus ln A (R = radius

of a nucleus and A = its mass number) is : (1) a straight line (2) a parabola (3) an ellipse (4) none of these Q. 18. A square coil ABCD with its plane vertical is released from rest in a horizontal uniform magnetic field B of length 2L. The acceleration of the coil is : A C B 2L

D

(1) 411/4 T (2) 511/4 T (3) 21/4 T (4) 371/4 T Q. 20. If a baseball player can throw a ball at maximum distance = d over a ground, the maximum vertical height to which he can throw it, will be (Ball has same initial speed in each case) : d (1) (2) d 2 d (3) 2d (4) 4

L

×

×

×

×

×

×

×

×

×

×

×

×

B

(1) less than g for all the time till the loop crosses the magnetic field completely (2) less than g when it enters the field and greater than g when it comes out of the field (3) g all the time (4) less than g when it enters and comes out of the field but equal to g when it is within the field Q.19. We have three identical perfectly black plates. The temperatures of first and third plate is T and 3T. What is the temperature of second plate if system is in equilibrium ?

Q. 21. A ball falls from a height of 1 m on a ground and it loses half its kinetic energy when it hits the ground. What would be the total distance covered by the ball after sufficiently long time ? Q. 22. Consider a gravity-free hall in which an experimenter of mass 50 kg is resting on a 5 kg pillow, 8 ft above the floor of the hall. He pushes the pillow down so that it starts falling at a speed of 8 ft/s. The pillow makes a perfectly elastic collision with the floor, rebounds and reaches the experimenter’s head. The time elapsed in the process is......s Q. 23. A battery of EMF 10V sets up a current of 1A when connected across a resistor of 8Ω. If the resistor is shunted by another 8Ω resistor, what would be the current in the circuit ? (in A) Q. 24. A liquid flows out drop by drop from a vessel through a vertical tube with an internal diameter of 2 mm, then the total number of drops that flows out during 10 grams of the liquid flow out..... [Assume that the diameter of the neck of a drop at the moment it breaks away is equal to the internal diameter of tube and surface tension is 0.02 N/m]. Q. 25. A cylinder of area 300 cm2 and length 10 cm made of material of specific gravity 0.8 is floated in water with its axis vertical. It is then pushed downward, so as to be just immersed. The work done by the agent who pushes the cylinder into the water is.....J.

184

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 26. A copper ball of density 8.6 g/cm3, 1 cm in diameter is immersed in oil of density 0.8 g/cm3. The charge in mC on the ball, if it remains just suspended in an electric field of intensity 3600 V/m acting in upward direction is..... mC. Q. 27. In a YDSE experiment two slits S1 and S2 have separation of d = 2 mm. The distance of the screen is D = 8/5 m. Source S starts moving from a very large distance towards S2 perpendicular to S1S2 as shown in figure. The wavelength of monochromatic light is 500 nm. The number of maximas observed on the screen at point P as the source moves towards S2 is 3995 + n. The value of n is..... S1 S

S2

d D

P

Q. 28. A leaky parallel plate capacitor is filled completely with a material having dielectric

constant K = 5 and electric conductivity s = 7.4 × 10–12 W–1 m–1. If the charge on the plate at the instant t = 0 is q = 8.85 mC, then the leakage current at the instant t = 12 s is………× 10–1 µA. Q. 29. Potential difference between the points A and B in the circuit shown is 16 V, then potential difference across 2Ω resistor is .….V. volt. (VA > VB)

4Ω

9V 1Ω

3V

1Ω

3Ω

A

B 2Ω

Q. 30. The half-value thickness of an absorber is defined as the thickness that will reduce exponentially the intensity of a beam of particles by a factor of 2. The half-value thickness in (mm) for lead assuming X-ray beam of wavelength 20 pm, m = 50 cm–1 for X-rays in lead at wavelength l = 20 pm, is..... mm

Chemistry Section A Q. 31. The chloride of a metal contains 71% chlorine by weight and the vapour density of it is 50. The atomic mass of the metal will be (valency of metal is 2) : (1) 29

(2) 58

(3) 35.5

(4) 71

Q. 32. Orthorhombic crystal has the following unit cell dimensions

(1) a ≠ b ≠ c and a = b = g ≠ 90°

(2) a ≠ b ≠ c and a = b = g = 90° (3) a ≠ b ≠ c and a = g = 90°, b ≠ 90° (4) a ≠ b ≠ c and a ≠ b ≠ g = 90° Q. 33. Which is low spin complex : (1) Fe(CN)64– (2) Co(NO2)63– 3– (3) Mn(CN)6 (4) All of these Q. 34. An inorganic salt solution gives a yellow precipitate with silver nitrate. The precipitate dissolves in dilute nitric acid as well as in ammonium hydroxide.

The solution contains : (1) Bromide (2) Iodide (3) Phosphate (4) Chromate Q. 35. The arrangement of oxygen atoms around phosphorus atoms in P4O10 is : (1) Pyramidal

(2) Octahedral

(3) Square planar (4) Tetrahedral Q. 36. Glucose with excess of phenyl hydrazine forms : (1) Fructosazone (2) Glucose phenyl hydrazone (3) Glucosazone (4) Phenyl hydrazone of glucosazone Q. 37. The correct set of the products obtained in the following reactions : reduction

(A) RCN

(B) RCN

(i) CH3MgBr

(C) RNC (D) RNH2

(ii) H2O hydrolysis HNO2

185

MOCK TEST PAPER-2

The answer is –



(1) A

B





2° Amine

Methyl ketone

C

D

Q. 39. If a compound on analysis was found to contain C = 18.5%, H = 1.55%, Cl = 55.04% and O = 24.81%, then its empirical formula is :

Alcohol

(1) CHClO

(2) CH2CIO

B

(3) C2H2OCl

(4) CICH2O

1° Amine

Methyl ketone



D

Q. 40. The major product of the following reaction is :



1°Amine



(2) A C

2° Amine

Alcohol

(3) A

B



2° Amine

Methyl ketone



C

D

(1) CH3O

2° Amine Acid

(4) A

B

2° Amine

Methyl ketone



C

D



2° Amine

Aldehyde

Q. 38. The major product of the following reaction is : N2Cl



(2) CH3O



(4) CH3O

OH

(1)

Me

Q. 41. H N=N



CH3

(3) CH3O

OH Base

CH3



Me OH + HO

Et

H Et B

OH

Me

Me

N=N

(2)

Et A

(2) Both SN2 (4) I SN2, II SN1

Q. 42. The correct order of bond strength is

N=N



H

HO

I

Steps I and II are : (1) Both SN1 (3) I SN1, II SN2

(3)

OH

(4)

OH

–

Et

OH



Cl

H

OH – II

N=N



− + 2− (1) O2 < O2 < O2 < O2



2 − + (2) O2 < O2 < O2 < O2



− 2− + (3) O2 < O2 < O2 < O2 + − 2− (4) O2 < O2 < O2 < O2

COOH OCOH

186

Oswaal JEE (Main) Mock Test 15 Sample Question Papers &

Q. 43. The enthalpy change states for the following processes are listed below: Cl2(g) = 2Cl (g)

242.3 kJ mol–1



I2(g) = 2I (g)

151 kJ mol

(1) 244.8 kJ mol



(2) –14.6 kJ mol

(3) –16.8 kJ mol (4) 16.8 kJ mol–1 Q. 44. In which delocalization of positive charge is possible : H H NH 3 N (1) (2)

OΘ

OH 2 (3)

(4)



Q. 45. The major Product of the following reaction is :

(1)

(2) (3)

(4) Q. 46. Which of the following order is correct : COOH OCOH



& OMe

functional isomer OEt

Et &

metamers Me

metamers

&

Me

CH2 – CH2 –OH CH 2 – O –CH 3 metamers

& Me –N–Me

CH2 –NH – CH 3

–1

–1





Given that the standard states for iodine chlorine are I2 (s) and Cl2 (g), the standard enthalpy of formation for ICl (g) is: –1

OEt Et

62.76 kJ mol–1

I2(s) = I2 (g)



OMe

242.3 kJ mol–1

ICl(g) = I (g) + Cl (g)

–1

functional isomer



&

functional isomers

(1) TFTF (2) FTTF (3) TTFT (4) TFFT Q. 47. Of the two solvent H2O and D2O, NaCl dissolves : (1) Equally in both the solvents (2) Only in H2O but remains insoluble in D2O (3) More in D2O (4) More in H2O Q. 48. In the electrolysis method of boron extraction the cathode is made of : (1) Carbon (2) Boric anhydride (3) Mg (4) Iron rod Q.49 Ge (II) compounds are powerful reducing agents, whereas Pb (IV) compounds are strong oxidants. It can be due to : (1) Lead is more electropositive than  germanium (2) The ionization potential of lead is less than that of germanium (3) The ionic radii of Pb2+ and Pb4+ are  larger than those of Ge2+ and Ge4+ (4)  More pronounced inert pair effect in lead than in germanium Q. 50. Which of the following statements is correct for CsBr3 ? (1) It is a covalent compound. (2) It contains Cs3+ and Br– ions. (3) It contains Cs+ and Br3– ions. (4) It contains Cs+, Br– and Br2 molecule.

Section B Q. 51. A drop of solution (volume 0.05 ml) contains 3.0 × 10–6 mole of H+. If the rate constant of disappearance of H+ is 1.0 × 107 mole l–1s–1. It would take for H+ in drop to disappear in..... × 10–9s

187

Mock Test Paper-2 Q. 52. The amount of C-14 isotope in a piece of wood is found to be 1/16th of its amount present in a fresh piece of wood. The age of wood, half-life period of C-14 is 5770 years, is.....years Q. 53. The overall formation constant for the reaction of 6 mol of CN– with Cobalt(II) is 1 × 1019. The formation constant for the reaction of 6 mol of CN– with Cobalt(III) is ..... X1063. Given that, –1 Co(CN)–3 Co(CN)6–4 6 + e

E°Rp = 0.83 V

Co+3 + e–1

Co+2



E°Rp = 1.82 V Q. 54. An element has body centered cubic structure with a cell edge of 3.0 Å. The density of the metal is 2 amu/Å3. Atoms present in 243 × 1024 amu of the element are ..... × 1024 Q. 55. Phenol associates in benzene to a certain extent to form a dimer. A solution containing 20 × 10–3 kg of phenol in 1.0 kg of benzene has its freezing point depressed by 0.69 K. The fraction of phenol that has dimerised is..... (Kf for benzene = 5.12 K kg mol–1) Q. 56. Finely divided catalyst has greater surface area and has greater catalytic activity than the compact solid. If a total surface area of

6291456 cm2 is required for adsorption of gaseous reaction in a catalysed reaction, then the number of splits should be made of a cube exactly 1 cm in length is..... [Given : After each split new cubes of equal dimensions are formed.] Q. 57. The first ionization energy of H is 21.79 × 10–19 J. The second ionization energy of He atom is...... × 10–19J Q. 58. E.N. of Si is..... (Covalent radius of Si = 1.175 Å) Q. 59. The number of p-bonds present in C2 (Vap.) molecule according to molecular orbital theory are..... Q. 60. In an experiment O3 undergo decomposition as O3 O2 + O by the radiations of wavelength 310 Å. The total energy falling on the O3 gas molecules is 2.4 × 1026 eV and quantum yield of the reaction is 0.2. The volume strength of the H2O2 solution which is obtained from reaction of 1 l H2O and nascent oxygen [O] obtained from the above reactions is..... (Assuming no change in volume of H2O) H2O + O H 2O2 [Given : NA (Avogadro's No.) = 6 × 1023

Mathematics Section A Q. 61. The co-ordinates of the point where the line joining the points (2, –3, 1), (3, –4, –5) cuts the plane 2x + y + z = 7 are : (1) (2, 1, 0) (2) (3, 2, 5) (3) (1, –2, 7) (4) None of these Q. 62. If D, E, F are the mid points of the sides BC, CA and Ab respectively of a triangle ABC and 'O' is any point, then, AD + BE + CF , is : (1) 1 (3) 2 dx Q. 63. ò x equals : e + e-x (1) log (ex + e–x) + c (3) tan–1 (ex) + c

(2) 0 (4) 4

(2) log (ex – e–x) + c (4) tan–1 (e–x) + c

1

Q. 64. ò|3x - 1| dx equals : 0

(1) 5/6

(2) 5/3

(3) 10/3

(4) 5

Q. 65. The area of the region bounded by the curve y = sin x and the x-axis in [–p, p] is : (1) 4

(2) 8

(3) 12 (4) 2 Q. 66. The curve passing through (0, 1) and satisfying sin æç dy ö÷ = 1 is: è dx ø 2

æ y+1 ö 1 (2) sin æ y - 1 ö = 1 (1) cos ç ç ÷ ÷= è x ø 2 è x ø 2 æ x ö 1 æ x ö 1 (3) cos ç ÷ = (4) sin ç ÷= è y +1ø 2 è y -1ø 2

188

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 67. If y = alog |x| + bx2 + x has its extremum values at x = –1 and x = 2, then : (1) a = 2, b = –1 (2) a = 2, b = -1 2 1 (3) a = –2, b = (4) a = –2, b = -1 2 2 q Q. 68. If x = a[cos θ + log tan ], y = a sin θ then 2 dy = dx (1) cos θ (2) sin θ (3) tan θ (4) cosec θ 1 Q. 69. The range of the function y = is : 2 - sin 3x æ1 3

ö

é1

ö

(1) çè , 1÷ø

(2) ê , 1÷ ë3 ø

é1 ù (3) ê 3 , 1ú ë û

æ1 ù (4) ç ,1ú è3 û

Q. 70. xlim ®-1

Q. 76. If log10 2 = 0.3010 ⋅ log103 = 0⋅4771 then number of ciphers after decimal before a -100 æ5ö significant figure comes in ç ÷ is è3ø

x 3 - 2x - 1 = x 5 - 2x - 1

1 2 (1) (2) 3 3 4 5 (3) (4) 3 3 Q. 71. A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point: (1) (3, 10) (2) (3, 5) (3) (2, 3) (4) (1, 5) Q. 72. If the line y – 3x + 3 = 0 cuts the parabola y2 = x + 2 at A and B, then PA. PB is equal to (where co-ordinates of P are ( 3 , 0)):

(

)

4 3 +2 (1) 3 (3) 2 3

(2) (4)

(

4 2- 3 2

(

3 3 +2

)

)

3 Q. 73. The tangent and the normal at a point P on y2 x2 an ellipse 2 + 2 = 1 meet its major axis in a b T and T' so that TT' = a then e2 cos2 θ + cos θ (where e is eccentricity of the ellipse) is equal to : (1) 1 (2) 1 2 1 2 (3) (4) 4 3 Comment As each nuclear less than 1, the sum can not be equal in 2 Q. 74. The asymptotes of the hyperbola xy = hx + ky are :

(1) x–k=0&y–h=0 (2) x+h=0&y+k=0 (3) x–k=0&y+h=0 (4) x+k=0&y–h=0 Q. 75. For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true ? (1) both roots are positive (2) both roots are negative (3)  roots have opposite sign, negative root has greater magnitude (4)  roots have opposite sign, positive root has greater magnitude

(1) 21 (2) 22 (3) 23 (4) 24 Q. 77. If the ratio of the sum of n terms of two AP’s is 2n : (n+1), then ratio of their 8th terms is : (1) 15 : 8 (2) 8 : 13 (3) 11:6 (4) 5 : 17 n 1ö æ Q. 78. If the 4th term in the expansion of ç ax + ÷ xø è 5 is then the values of a and n respectively 2 are : 1 (1) 2, 6 (2) ,6 2 1 (3) , 5 (4) 2, 5 2 Q. 79. The number of positive integers satisfying the inequality n + 1Cn – 2 – n + 1Cn – 1≤ 100 is : (1) Nine (2) Eight (3) Five (4) Ten Q. 80. If the orthocentre of the triangle formed by (1, 3) (4, –5) and (a, b) is (2, 4), Then the value of 33b + 22a is: (1) 0 (2) 1 11 (3) 1 (4) 3 11

Section B 1 sin n x + cosn x for n n = 1, 2, 3, ....... Then the value of

Q. 81. Given

fn ( x ) =

(

24(ƒ4(x) – ƒ6(x)) is equal to .....

)

189

Mock Test Paper-2 Q. 82. If the sum of all solutions of equation kp sin x + 2 cos x = 1 + 3 cos x in [0, 2p] is 6 The value of k is ..... Q. 83. The sum of the series

æ 2ö æ 1ö tan–1 ç ÷ + tan–1 çè ÷ø +..... è 3ø 9 é 2 n -1 ù –1  + tan ê 2 n - 1 ú +.......∞. ë1 + 2 û kp Then the value of k is....... is..... 4 Q. 84. If the number of five digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to.... Q. 85. In a workshop, there are five machines and the probability of any one of them to be out 1 of service on a day is . If the probability 4 that at most two machines will be out of 3

æ3ö service on the same day is ç ÷ k, then k is è4ø

continuous at x = 0 then (a2 + b2) is equal to.....



Q. 87. Four fair dice are thrown simultaneously. If probability that the highest number 25a obtained is 4 is then 'a' is equal to..... 1296 Q. 88. If the sides a, b, c of ∆ ABC satisfy the equation 4x3 – 24x2 + 47x – 30 = 0 and a2 ( s - b )2 ( s - c )2

é 0 aa 2 ab2 ù ê ú Q. 89. If D = êba + c 0 ag 2 ú is a skew ê bb + c ( b g + c ) 0 ú ë û symmetric matrix (where α, β, γ are distinct) ( a + 1)2 and the value of (3 + c ) (3 - b )2

Q. 86. If function



( s - a )2 p2 where p and q ( s - b )2 = q 2 c

are co-prime and s is semiperimeter of ∆ABC, then the value of (p – q) is.....

equal to...........

ì a sin x + b tan x – 3 x , x¹ 0 ï ƒ( x ) = í x3 is ïî 0 , x =0

( s - a )2 b2 ( s - c )2

(1 - a) ( b + 2)2 b2

(2 - c ) ( b + 1)2 ( c + 3)

is λ then the value of |10 l| is..... Q. 90. Let |z| = |z – 3| = |z – 4i|, then the value|2z| is.....

Answers Physics Q. No.

Answer

1

(3)

2

Topic’s Name

Q. No.

Answer

Topic’s Name

Vector

16

(4)

Atomic Structure

(2)

Unit & Dimension

17

(1)

Nuclear Physics

3

(1)

One Dimension

18

(4)

Electromagnetic Induction

4

(2)

Newton's Law of Motion

19

(1)

Stefan's Law

5

(4)

Circular Motion

20

(1)

Projectile Motion

6

(4)

Work Energy and Power

21

3.00

Coefficient of Restitution

7

(3)

Rotational

22

2.22

Conservation Law

8

(3)

Simple Harmonic Motion

23

1.67

Electricity

9

(1)

Properties of Matter

24

780

Surface Tension

10

(2)

Doppler Effect

25

0.06

Fluid Mechanics

11

(3)

Wave Optics

26

34.00

Electrostatics

12

(2)

Refraction at Curved Surface

27

5.00

Gauss’s Law

13

(1)

Prism

28

2.00

Capacitance

14

(2)

Alternating Currents

29

6.00

Current Electricity

15

(3)

Semiconductors

30

139

X-rays

190

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Chemistry Q. No. 31

Answer (1)

32

(2)

33

(4)

34 35

Topic’s Name Mole Concept

Q. No. 46

Answer (3)

Topic’s Name Isomerism

Solid state

47

(4)

Hydrogen Family

Coordination Compound

48

(4)

Boron Family

(3)

Salt Analysis

49

(4)

Carbon Family

(4)

Nitrogen Family

50

(3)

s-Block Elements

36

(3)

Biomolecules & Polymer

51

6.00

Chemical Kinetics

37

(2)

Nitrogen Compound

52

23080

Nuclear Chemistry

38

(1)

Nitrogen compound

53

1.81

39

(1)

Basic Concepts

54

9.00

Solid State

40

(4)

Haloalkane

55

0.733

Solution

41

(4)

Halogen Dervatives

56

20.00

Surface Chemistry

42

(2)

Aromatic Chemistry

57

87.16

Atomic Structure

43

(4)

Thermodynamics

58

1.823

Periodic Table

44

(4)

General Organic Chemistry

59

2.00

Chemical Bonding

45

(2)

Classification & Nomenclature

60

22.40

Gaseous State

Electrochemistry

Mathematics Q. No.

Answer

61

(3)

62

Topic’s Name

Q. No.

Answer

Three Dimentional Geometry

76

(2)

Logarithems

(2)

Vector

77

(1)

Progressions

63

(3)

Indefinite Integration

78

(2)

Binomial Theorem

64

(1)

Definite Integration

79

(1)

Purmutation and Combinations

65 66

(1) (2)

80 81

(3) 2.00

Point and Straight Line Trigonometric Ratios

67

(2)

82

5.00

Trigonometric Equation

68 69

(3) (3)

Area Under Curve Differential Equations Application of Derivatives Maxima & Minima Differentiation Functions

83 84

1.00 8

Inverse Trigonometric Functions Permutation and combination

70

(2)

Limits

85

17 8

Probability

71

(1)

Circles

86

5.00

Continuity

72

(1)

Parabola

87

7.00

Probability

73

(1)

Ellipse

88

7.00

Determinants

74

(1)

Hyperbola

89

600

Matries

75

(3)

Quadratic Equations

90

5.00

Complex Numbers

–

Topic’s Name



3

MOCK TEST PAPER Time : 3 Hours

Total Marks : 300

General Instructions : 1. 2. 3. 4. 5. 6.

There are three subjects in the question paper consisting of Physics (Q. no. 1 to 30), Chemistry (Q. no. 31 to 60) and Mathematics (Q. no. 61 to 90). Each subject is divided into two sections. Section A consists of 20 multiple choice questions & Section B consists of 10 numerical value type questions. In Section B, candidates have to attempt any five questions out of 10. There will be only one correct choice in the given four choices in Section A. For each question 4 marks will be awarded for correct choice, 1 mark will be deducted for incorrect choice for Section A questions and zero mark will be awarded for not attempted question. For Section B questions, 4 marks will be awarded for correct answer and zero for unattempted and incorrect answer. Any textual, printed or written material, mobile phones, calculator etc. is not allowed for the students appearing for the test. All calculations / written work should be done in the rough sheet is provided with Question Paper.

Physics Section A Q. 1. A projectile is fired with a speed u at an angle q above the horizontal field. The coefficient of restitution between the projectile and field is e. Find the position from the starting point when the projectile will land at its second collision e 2 u2 sin 2q (1) g

(1 - e ) u 2



(2)

(3) (4)

2

g

(1 + e ) u

Q. 3. At an instant t, the coordinates of a particle are x = at2, y = bt2 and z = 0, then its velocity at the instant t will be : (1) t a 2 + b 2

sin 2q

g (1 - e ) u2 sin q cos q 2

2

é ù é ù m1 m1 (1) d ê ú (2) d ê ú ëê ( m1 + m2 ) ûú ëê ( m1 + m2 ) ûú 2 é ( m1 + m2 )2 ù é ù m2 ú (4) d ê (3) d ê ú m2 êë úû êë ( m1 + m2 ) úû

sin 2q

g Q. 2. Two pendulums each of length l are initially situated as shown in figure. The first pendulum is released and strikes the second. Assume that the collision is completely inelastic and neglect the mass of the string and any frictional effects. How high does the centre of mass rise after the collision?

2 (3) a 2 + b 2 (4) 2t a 2 + b 2 Q. 4. What is the average velocity of a projectile between the instants it crosses half the maximum height, if it is projected with a speed u at an angle θ with the horizontal :

(1) u sin θ

F

+2 0

l

(2) u cos θ

(3) u tan θ (4) u Q. 5. A force - time graph for the motion of a body is shown in figure. Change in linear momentum between 0 and 8 s is :

(in N)

m1

(2) 2t a 2 + b 2

6

2 4

l –2

d m2

t in s

8

192

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

(1) zero

(2) 4 N-s

(3) 8 N-s (4) None Q. 6. For the arrangement shown in figure, the tension in the string to prevent it from sliding down, is : m = 1 kg µ = 0.8 37°

(1) 6 N

(2) 6.4 N

(3) 0.4 N (4) None of these Q. 7. Two small balls each having equal positive charge Q are suspended by two insulating strings at equal length L metre, from a hook fixed to a stand. The whole set-up is taken in a satellite into space where there is no gravity. Then the angle θ between two strings and tension in each string is : Stand L Q

(1) 0,

kq 2 L2

L Q

(2) p,

kq 2 2 L2

p kq 2 kq 2 (4) , 2 2 L2 4 L2 Q. 8. A charge Q is uniformly distributed over a large plastic plate. The electric field at a point P close to the centre of the plate is 10 V/m. If the plastic plate is replaced by a copper plate of the same geometrical dimensions and carrying the same charge Q, the electric field at the point P will become : (3) p,

(1) Zero

(2) 5 V/m

(3) 10 V/m (4) 20 V/m Q. 9. In copper, each copper atom releases one electron. If a current of 1.1 A is flowing in the copper wire of uniform cross-sectional area of diameter 1 mm, then drift velocity of electrons will approximately be : (Density of 3 3 copper = 9 × 10 kg /m , Atomic weight of copper = 63) (1) 10.3 mm/s

turns. Find the ratio of magnetic induction at centre in above two cases. 2 (2) 1 : n2 (1) 4 : n 2 2 (3) 1 : n (4) 2 : n Q. 11. Two plane mirrors are parallel to each other and spaced 20 cm apart. An object is kept in between them at 15 cm from A. Out of the following at which point image is not formed in mirror A (distance measured from mirror A) : (1) 15 cm (2) 25 cm (3) 45 cm (4) 55 cm Q. 12. In a certain double slit experimental arrangement, interference fringes of width 1.0 mm each are observed when light of wavelength 5000 Å is used. Keeping the set-up unaltered if the source is replaced by another of wavelength 6000 Å, the fringe width will be : (1) 0.5 mm (2) 1.00 mm (3) 1.2 mm (4) 1.5 mm Q. 13. In a vernier callipers, ten smallest divisions of the vernier scale are equal to nine smallest division on the main scale. If the smallest division on the main scale is half millimeter, then the Least Count of Vernier Callipers is : (1) 0.5 mm (2) 0.1 mm (3) 0.05 mm (4) 0.005 mm Q. 14. Two media I and II are separated by a plane 8 surface having speeds of light 2 × 10 m/s 8 and 2.4 ×10 m/s, respectively. What is the critical angle for a ray going from I medium to II ? æ5ö –1 æ 1 ö (2) sin–1 ç ÷ (1) sin ç ÷ 2 è ø è6ø

æ 1 ö æ 5 ö (3) sin–1 ç ÷ (4) sin–1 ç ÷ è 12 ø è 2ø Q. 15. A ray of light is incident on a prism ABC (AB = BC) and travels as shown in figure. The refractive index of the prism material should be at least : A 90º 90º B

(2) 0.1 mm/s

(3) 0.2 mm/s (4) 0.2 cm/s Q. 10. A wire of length L carrying current i is bent into circular loop with (i) one turn (ii) n

4 3 (3) 1.5 (1)

90º C

(2)

2

(4)

3

193

Mock Test PAPER-3 Q. 16. A trapezium is made up of sides of length 5cm, 5cm, 5cm and 10 cm. A ray is incident



On the Slant face of the trapezium such that it emerges through the other slant face. (Given that i=e=45°) what is the angle of deviation of the ray ?

(1) 60°

(2) 30°

(3) 37° (4) 53° Q. 17. If n >1, then the dependence of frequency of a photon, emitted as a result of transition of electron from nth orbit to (n–1)th orbit, on n will be : 1 1 (1) υ ∝ (2) υ ∝ 2 n n 1 1 (3) υ ∝ 3 (4) υ ∝ 3 v n Q. 18. A proton moving with velocity v0 moves towards a proton initially at rest and free to move. Find the distance of closest approach. (1)

e2 2 pe 0 mv02

(2)

e2 4 pe0 mv02

(3)

e2 pe 0 mv02

(4) None of these

Q. 19. Photoelectric emission is observed from a metallic surface for frequencies ν1 and ν2 of the incident light rays (ν1 > ν2). If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio of 1 : k, then the threshold frequency of the metallic surface is : k n1 - n2 n - n2 (2) (1) 1 k -1 k -1 k n2 - n1 k -1

n2 - n1 k Q. 20. A source of frequency n and an observer are moving on a straight line with velocities a and b, respectively. If the source is ahead of the observer and if the medium is also moving in the direction of their motion with velocity c (the velocity of sound being v) then the apparent frequency of sound heard by the observer would be æv-c+bö æv+c+bö (2) ç (1) ç ÷n ÷ v + c + a èv-c+aø è ø

(3)

æ v-c-bö (3) ç ÷n èv-c-aø

(4)

æ v+c-bö (4) ç ÷n èv+c-aø

Section B Q. 21. A motor car is travelling at 60 m/s on a circular road of radius 1200 m. It is increasing its speed at the rate of 4 m/s2. The acceleration of the car is ............ m/s2. Q. 22. A 10 kg block is initially at rest on a horizontal surface for which the coefficient of friction is 0.5. If a horizontal force F is applied such that it varies with time as shown in figure. The work done (in joule) in first 5 s is 225 α. The value of α is ............ J. (g = 10 ms–2) F (in N) 100

t (in s)

6 0 2 4 Q. 23. In the figure below, a uniformly piece of wire is bent in the form of a semicircular arc as shown. Find the distance (in cm) of center of mass of the wire from the origin is .......... cm, if radius of the semicircular ring is R = 3π cm. y

x

Q. 24. Figure shows the variation of the moment of inertia of a uniform rod, about an axis passing through its centre and inclined at an angle θ to the length. The moment of inertia (in kg-m2) of the rod about an axis passing through one of its ends and making an angle p 2 q = rad will be ............ kg-m . 3 1 I(kg-m2) π θ(rad) Q.25. Binary stars of comparable masses m1 and m2 rotate under the influence of each other’s gravity with angular velocity ω. If they are stopped suddenly in their motions, their relative velocity when they collide with each

other is

a é 2G ( m + m ) æ ö ù w2 1 2 ê ú -ç ç G ( m + m ) ÷÷ ú ê ( R1 + R 2 ) 1 2 ø è ë û

b

194

Oswaal JEE (Main) Mock Test 15 Sample Question Papers loses its contact with the platform when its angular frequency is 5 rad/s. The amplitude of vibration can not be less than ‘A’ cm, then The value of A is ............ cm.

where R1 and R2 are radii of stars and G is the universal gravitational constant. The 3

æ 1 1ö value of ç + ÷ is ........... èa bø Q.26. A rubber cord has a cross–sectional area 1 mm2 and total unstretched length 10 cm. It is stretched to 12 cm and then released to project a mass of 5 g. The Young's modulus for rubber is 5 × 108 N–m2. The velocity of mass is ........... m s–1.

Q. 27. A U-tube having uniform cross-section but unequal arm length l1 = 100 cm and l2 = 50 cm has same liquid of density r1 filled in it upto a height h = 30 cm as shown in figure. Another liquid of density r2 = 2r1 is poured in arm A. Both liquids are immiscible. The length of the second liquid is .......... (in cm) should be poured in A so that second overtone of A is in unison with fundamental tone of B. (Neglect end correction) A

n

B

1

Q.29. A thermometer has a spherical bulb of 3 3 volume 1 cm having 1 cm of mercury. A long cylindrical capillary tube is connected to spherical bulb. Volumetric coefficient –4 –1 of expansion of mercury is 1.8 × 10 K ; –4 cross-section area of capillary is 1.8 × 10 2 cm . Ignoring expansion of glass, .......... cm far apart on the stem are marks indicating 1K temperature change.

1

2

h Q. 28. A block is placed on a horizontal platform vibrating up and down, simple harmonically. It is observed that the block

Q. 30. A uniform disc of radius R having charge Q distributed uniformly all over its surface is placed on a smooth horizontal surface. A 2 magnetic field B = Kxt , where K = constant, x is the distance (in metre) from the centre of the disc and t is the time (in second) is switched on perpendicular to the plane of the disc. The torque (in N-m) acting on the disc after 15 sec. (Take 2 KQ = 1 S.I. unit and R = 1 metre) is ...........N-m.

Chemistry Section A Q. 31. A reaction required three atoms of Mg for two atoms of N. How many g of N are required for 3.6 gm of Mg ? (1) 2.43 (2) 4.86 (3) 1.4 (4) 4.25 Q. 32. Which of the following pairs of specis have the same bond order (1) N2, NO+ (2) O2, NO+ (3) N 2 , O2

(4) CO, NO

Q. 33. Calculate the ground state energies of the + 2+ electron (in eV) in the case of He and Li (RH = 13.6 eV) (1) – 13.60 eV and –54.40 eV (2) –54.40 eV and –13.60 eV (3) –54.40 eV and –122.40 eV (4) –13.60 eV and –122.40 eV Q. 34. The element Z = 107 and Z = 109 have been made recently; element Z = 108 has not yet been made. Indicate the group in which you will place the above elements. (1) 7, 8, 9 (2) 5, 6, 7 (3) 8, 9, 10 (4) 4, 5, 6

195

Mock Test PAPER-3 CO

Q. 35. P= 7 atm V= 10 00 ml

P= 10 atm V= 800 ml Fig II

Fig I



In the above figures a doll is entrapped within a piston and cylinder containing gas. Initial and final conditions are shown Figure I and Figure II respectively. The volume of doll is : 15000 (1) 1000 ml (2) ml 17 1000 1000 (3) ml (4) ml 3 15 Q. 36. Enthalpy of fusion of a liquid is 1.435 kcal mol–1 and molar entropy change is 5.26 cal mol–1K–1. Hence melting point of liquid is : (1) 100°C (2) 0°C (3) 373°C (4) –273°C Q. 37. In Fe 4 éë Fe ( CN )6 ùû 3 the O.N. of the complexed iron is : (1) + 3 (2) + 2 (3) + 4 (4) + 6 Q. 38. For the gas phase reaction C2H4 + H2  C2H6, DH = –32.7 kcal carried out in a vessel, the equilibrium concentration of C2H4 can be increased by (1) Increasing the temperature (2) Increasing concentration of H2 (3) Decreasing temperature (4) Increasing pressure Q. 39. The following equilibrium is established when hydrogen chloride is dissolved in acetic acid HCl + CH3COOH  Cl– + CH3 COOH2+. The set that characterises the conjugate acid-base pairs is : (1) (HCl, CH3COOH) and (CH3COOH2+, Cl–) (2) (HCl, CH3COOH2+) and (CH3COOH, Cl–) (3) (CH2COOH2+, HCl) and (Cl–, CH3COOH) (4) (HCl, Cl–) and (CH3COOH2+, CH3COOH) Q. 40. Ethyl methyl vinyl amine has the structure :

Q. 41. The correct name of (CO)3 Fe – CO – Fe(CO)3 is : CO (1) Tri-µ-carbonyl bis (tricarbonyl iron (0) (2)  Hexacarbonyl iron (III) µ-tricarbonyl ferrate (0) (3) Tricarbonyl iron (0) µ-tricarbonyl iron (0) tricarbonyl (4) Nonacarbonyl iron Q. 42. The complex that has lowest magnetic moment is: 2– (1) [NiCl4]

(3) [Mn (Cn)6]3– (4) [Ni (CO)4] Q. 43. Concentration of ore of Aluminium is done by (1) Froth floatation (2) Gravity separation (3) Baeyer’s process (4) Magnetic separation Q. 44. The major product of the following reaction is:



(1) (2)



(3)





(4) Q. 45. The product formed when adipic acid is heated : COOH

(1)

(2)

C=O

O (3)

(2) CH3CH2–N–CH=CH2

COOH

O

(4) COOH

O

CH3 (3) CH2=CH–N–CH=CH2

Q. 46.

CH3 (4) CH3–N–CH=CH2

O product (A) is

CH3



CH3 | CH — NH2



(1) CH3CH2–N–CH2CH=CH2 CH3

(2) [CoF6]3–

C – NH2

Br2 / KOH

A

196

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

(1)

COOH (2)

NH2

Q. 55. A mineral of iron contains an oxide containing 72.36% iron by mass and has a density of 5.2 g/cc. Its unit cell is cubic with

(3)

Br

(4) None of these

edge length of 839 pm. The total number of atoms (ions) present in each unit cell is

X) Q. 47. (C6H12O5)n + nH2O ¾(¾ ® Y) C12H22O11 + H2O ¾(¾ ® 2C6H12O6 Enzymes X and Y are : (1) Zymase and Invertase (2) Diatase and Maltase (3) Maltase and Diatase (4) Diatase and Zymase Q. 48. Pure chlorine is obtained : (1) by heating PtCl4 (2) by heating MnO2 with HCl (3) by heating bleaching powder with HCl (4) by heating mixture of NaCl, MnO2 and Conc. H2SO4 Q. 49. In the Hunsdiecker reaction : (1) Number of carbon atoms decrease (2) Number of carbon atoms increase (3) Number of carbon atoms remain same (4) None of the above H2 O Q. 50. In the reaction sequence, CaC2 A H2 dil. H2SO4 B C, the product C is : +2

........... (Fe-56, O-16) Q. 56. An organic liquid, A, is immiscible with water. When boiled together with water, the boiling point is 90ºC at which the partial vapour pressure of water is 526 mm Hg. The atmospheric pressure is 736 mm Hg. The weight ratio of the liquid and water collected is 2.5 : 1. The molecular weight of the liquid is ........... gm. Q. 57. Graph between log x/m and log p is straight line inclined at an angle of 45°. When pressure is 0.5 atm and lnk = 0.693, the amount of solute adsorbed per gm of adsorbent will be ........... Q. 58. Fixed amount of an ideal gas contained in a sealed rigid vessel (V = 24.6 litre) at 1.0 bar is heated reversibly from 27°C to 127°C. The change in Gibb's energy is ........... J (| ∆G | in Joule) if entropy of gas

Ni

Hg

(1) CH3OH (3) C2H5OH

(2) CH3CHO (4) C2H4

S = 10 + 10

Q. 52. Cyclohexane-1,4-dione is a polar compound, having dipole moment value of 1.2 D. If mol fraction of its chair form is 0.80, the dipole moment of twisted boat form will be ........... Q. 53. For 24Na, t1/2 = 14.8 hours. A sample of this substance lose 90% of its radioactive intensity will take .......... hr. Q. 54. The potential of the standard IronCadmium cell is .......... V, after the reaction has proceeded to 80% completion. Initially 1 M of each taken and Eº for cell = 0.04 V.

T (J/K)

Q. 59. The following sequence of reaction occurs in commercial production of aqueous nitric

Section B Q. 51. Given that the temperature coefficient for the saponification of ethyl acetate by NaOH is 1.75. The activation energy for the saponifiocation of ethyl acetate is ........... K. cal mol–1.

–2

acid. 4NH3(g) + 5O2(g) → 4NO(g) + 6H2O(l) DH = –904 kJ   ... (1)



2NO(g) + O2(g) → 2NO2(g) DH = –1124 kJ   ... (2)



3NO2(g) + H2O(l) → 2HNO3(aq) + NO(g) 

DH = –140 kJ   ... (3)



The total heat liberated (in kJ) at constant pressure for the production of exactly 1 mole of aqueous nitric acid by this process, is .......... kJ/mol.

Q. 60. The quantity of benzene, when 91.2 gm of Phenylmagnesium iodide is treated with 4.2 gm of Pent-4-yn-1-ol at STP would be produced ........... .

197

Mock Test PAPER-3

Mathematics Section A

(3)

sin 7 x + 6 sin 5x + 17 sin 3x + 12 sin x = sin 6 x + 5 sin 4 x + 12 sin 2 x (1) cos x (2) 2 cos x (3) sin x (4) 2 sin x Q. 62. The general solution of x when 2cos  x . cos 2x = cos x is :

Q.61

p p or kπ ± , n, k ∈ I 6 2 p (2) nπ ± π or kπ ± , n, k ∈ I 3 p (3) (2n + 1)π or kπ ± , n, k ∈ I 2 p p or k p ± , n, k ∈ I (4) np + 4 3 é æ 1 öù Q. 63. The value of sin êarc cos ç - ÷ ú is : è 2 øû ë 1 (1) (2) 1 2

(1) np +

(3)

3 2

(4)

æp pö Q. 65. For any θ ∈ ç , ÷ the expression è4 2ø 3(sinθ – cos θ)4 + 6(sin θ + cos θ)2 + 4sin6 θ equals: (1) 13 – 4cos2θ + 6sin2θcos2θ (2) 13 – 4cos6θ (3) 13 – 4cos2θ + 6cos4θ (4) 13 – 4cos4θ + 2sin2θ cos2θ 2

Q. 66. If a + 4b = 12ab, then log (a + 2b) =

1 (log a + log b – log 2) 2 a b + log + log 2 (2) log 2 2 (1)

1 (log a – log b + 4 log 2) 2 Q. 67 Graph of the function f(x) = Ax2 – Bx + C, where A = (sec q – cos q) (cosec q – sin q) (tan q + cot q), B = (sin q + cosec q)2 + (cos q + sec q)2 – (tan2 q + cot2 q) and C = 12, can be represented by : (4)

(1)

y

x

(2)

y

x

3

a2 - b 2 Q. 64. If in a triangle ABC, in usual notation 2 a + b2 sin ( A - B ) = , then the triangle is : sin ( A + B ) (1) Right angled or isosceles (2) Right angled and isosceles (3) Equilateral (4) Isosceles only

2

1 (log a + log b + 4 log 2) 2

(3)

y

x

(4)

y

x

Q. 68. The sum of all even positive integers less than 200 which are not divisible by 6 is : (1) 6534 (2) 6354 (3) 3456 (4) 6454 Q. 69. If the angle between the circles x2 + y2 – 2x + 4y – 4 = 0 and x2 + y2 – 8x – 2y + 8 = 0 is q, then the value of cos 2q is : -1 (1) 1 (2) 2 (3) 0

(4)

3 2

198

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 70. The numerically greatest terms in the 1 expansion of (3 – 5x)15 when x = are : 5 (1) T4, T5 (2) T5, T6 (3) T6, T7

(4) T3, T4

pü ì p Q. 71. If A = íx : £ x £ ý and 3þ î 6 f(x) = cos x – x (1 + x) then f(A) is equal to :

(1) 400 2

(2) 800 2

(3) 0

(4)

2 Q. 75. The area (in sq. units) of the region A = {(x, y) : (x – 1) [x] ≤ y ≤ 2 x , 0 ≤ x ≤ 2}, where [t] denotes the greatest integer function, is : (1)

ép pù (1) ê , ú ë6 3û

400

8 1 23 2

(2)

8 2 -1 3

4 2 +1 3

4 1 22 3

pù é p (2) ê - , - ú 6û ë 3

(3)

é ù (3) ê 1 - p æç 1 + p ö÷ , 3 - p æç 1 + p ö÷ ú 3ø 2 6è 6 øû ë2 3 è

Q. 76. The differential equation of the family of 2 curves, x = 4b(y + b), b ∈ R, is:

é ù (4) ê 1 + p æç 1 - p ö÷ , 3 + p æç 1 - p ö÷ ú 3ø 2 6è 6 øû ë2 3 è

Q. 72. If a function f(x) defined by ìae + be ïï f f(x) ( x ) í cx 2 ï 2 ïî ax + 2 cx x



Q. 73

-x

, 3>x£4

(1) –1

åi

n!

n=0

equals (where i =

-1 )

(2) i (4) 97 + i

statement about the matrix A is 2 (1) A = I

(2) A = (–1) I, where I is a unit matrix –1 (3) A does not exist

(4) A is a zero matrix é4 Q. 79. If A = ê -1 2 ë (1) A + 6I

2ù then (A– 2I) (A – 3I) equals : 1 úû (2) I

1

(3) Zero matrix (4) 6I         Q. 80. Points a + b + c , 4 a + 3b , 10 a + 7 b - 2 c are :

æ tan x ö tan -1 ç ÷+c 3 è 3 ø

(1) collinear

(2) non-coplanar

(3) non-collinear

(4) form a triangle

æ 2 tan x ö tan -1 ç ÷+c 2 3 3 ø è 1

1 tan–1 (2 tan x) + c 2 1 (4) tan -1 3 tan x + c 2

(

)

400 p

0

Q. 77. The value of

æ 0 0 -1 ö ç ÷ Q. 78. Let A = ç 0 -1 0 ÷ . The only correct ç -1 0 0 ÷ è ø

dx

ò

100

, 1£x £3

(3)

Q. 74

2 (4) x(y') = x – 2yy′

(3) xy'' = y'

(3) 2i + 95

ò 3 + sin 2x equals :

(2)

2 2 (1) x(y') = x + 2yy' (2) x(y') = 2yy′ – x

, -1 £ x < 1

be continuous or some a, b, c ∈ R and f′(0) + f′(2) = e, then the value of a is : 1 e (1) 2 (2) 2 e - 3e + 13 e - 3e - 13 e e (3) 2 (4) 2 e + 3e + 13 e 3 e + 13

(1)

(4)

1 - cos 2 x dx is equal to :

Section B Q. 81. If 'k' is the least distance between the curves 2 2 2 y = 6x and x + y – 16x + 60 = 0, then the value of [k], is ..........., where [.] denotes the greatest integer function.

199

Mock Test PAPER-3 Q. 82. If the area of the quadrilateral formed by the 2 2 common tangents of the circle x + y = 25 2 2 y x = 1 is A. Then the and the ellipse + 36 16

(

)

value of 3 11A - 1 is ........... Q. 83. If area of the triangle formed by latus rectum and tangents at the end points of latus x2 y2 = 1 is A, then 80 A is .......... rectum of 16 9 Q. 84. Given a regular tetrahdedron OABC with side length 1 unit. Let D and E are mid points m of AB and OC respectively. If DE + AC = p n (where m and n are coprime), then (m + n) is ........... Q. 85. An unbiased coin is tossed indefinitely. Probability that the fourth head is obtained on k , then 'k' is equal to ........... the sixth toss is 32 Q. 86. Let ƒ(x) = [[x] + {x2}] + {[x2] + {x}}, then number of points where |ƒ(x)| is non-

derivable in [–3, 3] is equal to ........... (where [.] denotes greatest integer function and {.} denotes fractional part function) Q. 87. Let ƒ(x) = (lnx)x + ln(xx) + xlnx, then ƒ'(e) is equal to ........... Q. 88. If m is the slope of a line which is tangent to y3 = x4 and a normal to x2 – 2x + y2 = 0, then 3 æ 3m ö is equal to ........... (m ≠ 0) ç 4 ÷ è ø Q. 89. Out of m errors in a computer program Mr. A found 200 errors and Mr. B found 125 errors. 50 errors are common in finding of both A and B, if probability of "neither A 2 nor B" found any error is , then value of 7 'm' is ........... Q. 90. Maximum distance between the plane 2x + y + 2z = 3 and the circle on the xy-plane a 2 2 , then the x + y – 2x – 2y + 1 = 0 is b value of (a + b) is ........... (a, b are coprime natural numbers)

Answers Physics Q. No.

Answer

Q. No.

Answer

1

(4)

Topic Name Basic Math & Vector

16

(2)

Refraction at curve surface

Topic Name

2

(1)

Unit and Dimension

17

(3)

Atomic Structure

3

(2)

One dimension

18

(3)

Nuclear Physics

4

(2)

Projectile Motion

19

(2)

Photo electric effect

5

(1)

Newton's Law of Motion

20

(2)

Doppler Effect

6

(4)

Friction

21

5.00

Circular Motion

7

(3)

Electrostatics

22

1125

Work Energy and Power

8

(2)

Capacitance

23

6.00

Momentum

9

(2)

Current Electricity

24

3.00

Rotational Motion

10

(3)

Magnetic effect of current

25

125

Gravitation

11

(3)

Reflection of Plane & Curve Surface

26

20.00

Elasticity

12

(3)

Wave Optics

27

6.00

Fluid Mech

13

(3)

Practical Physics

28

40.00

Simple Harmonic Motion

14

(2)

Refraction at Plane Surface

29

1.00

Heat & Thermo

15

(2)

Prism

30

3.00

EMI

200

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Chemistry Q. No.

Answer

31

(3)

32

(1)

33

Topic Name

Q. No.

Answer

Topic Name

Mole Concept

46

(2)

Nitrogen Compound

Chemical Bonding

47

(2)

Biomolecules

(3)

Atomic Structure

48

(1)

Halogen Family

34

(1)

Periodic Table

49

(1)

Halogen Derivatives

35

(3)

Gaseous State

50

(3)

Alcohol, Ether and Phenol

36

(2)

Chemical Energetics

51

10.70

Chemical Kinetics

37

(2)

Redox Reaction

52

0.20

Isomerism

38

(1)

Chemical Equilibrium

53

49.17

Nuclear Chemistry

39

(4)

Acid, bases, ionic equilibrium

54

0.01

Electrochemistry

40

(2)

IUPAC

55

56.00

Solid State

41

(1)

Coordination Compound

56

112.70

Solution

42

(4)

Coordination Compound

57

1.00

Surface Chemistry

43

(3)

Metallurgy

58

530

Thermodynamics

44

(3)

Carbonyl Compound

59

493

Thermo-chemistry

45

(2)

Carboxylic Acid

60

2.24

Aromatic Compound

Mathematics Q. No.

Answer

61

(2)

Topic Name Trigonometric Ratios

Q. No.

Answer

76

(1)

Topic Name

62

(1)

Trigonometric Equation

77

(3)

Complex Numbers

63

(3)

Inverse Trigonometric Functions

78

(2)

Determinant

64

(1)

Properties of Triangle

79

(3)

Matrices

65

(1)

Properties of Triangle

80

(1)

Vectors

66

(3)

Logarithm

81

4.00

Parabola

67

(2)

Quadratic Equation

82

999.00

Ellipse

68

(1)

Progressions

83

324.00

Hyperbola

69

(1)

Circles

84

4.00

Vectors

70

(1)

Binomial Theorem

85

5.00

Probability

71

(3)

Functions

86

1.00

Continuity-Differentiability

72

(2)

Limit

87

5.00

Differentiation

73

(1)

Indefinite Integration

88

4.00

Application of Derivatives

74

(2)

Definite Integration

89

385.00

75

(2)

Area Under Curve

90

8.00

Differential Equations

Permutation and Combination Three Dimensional Plane



MOCK TEST PAPER Time : 3 Hours

4 Total Marks : 300

General Instructions : 1. 2. 3. 4. 5. 6.

There are three subjects in the question paper consisting of Physics (Q. no. 1 to 30), Chemistry (Q. no. 31 to 60) and Mathematics (Q. no. 61 to 90). Each subject is divided into two sections. Section A consists of 20 multiple choice questions & Section B consists of 10 numerical value type questions. In Section B, candidates have to attempt any five questions out of 10. There will be only one correct choice in the given four choices in Section A. For each question 4 marks will be awarded for correct choice, 1 mark will be deducted for incorrect choice for Section A questions and zero mark will be awarded for not attempted question. For Section B questions, 4 marks will be awarded for correct answer and zero for unattempted and incorrect answer. Any textual, printed or written material, mobile phones, calculator etc. is not allowed for the students appearing for the test. All calculations / written work should be done in the rough sheet is provided with Question Paper.

Physics Section A Q. 1. The main scale of a spectrometer is divided into 720 division in all. If circular vernier scale consists of 30 divisions, the least count of the instrument is (Given : 30 vernier divisions coincide with 29 main scale divisions) (1) 0.1° (2) 1’’ (3) 1’ (4) 0.1’’ Q. 2. Photoelectrons are observed to just emit out of a material surface when the light of 620 nm falls on it with the intensity of 100 W m–2. If the light of wavelength 400 nm is incident on the same material with an intensity of 1 W m–2, what would be the minimum reverse potential needed to stop the outflow of the electrons? (1) 1 V (2) 2 V (3) 1.2 V (4) 1.9 V Q. 3. A certain element decays in two different ways – it shows alpha decay with a half life of (ln 2) years and with beta decay, it has a half life of (ln 4) years. After how many years will a pure sample of 100 mg of the element would have 50 mg of that element? (1) 0.52 years (2) 0. 46 years (3) 0.75 years (4) 1.25 years Q. 4. Find the binding energy of a H-atom in the state n = 2 (1) 2.1 eV (2) 3.4 eV (3) 4.2 eV (4) 2.8 eV

Q. 5. Figure represents a square carrying charges +q, +q, –q, –q at its four corners as shown. Then the potential will be zero at points +q A



–q

P

B Q

+q C –q

(1) A, B, C, P and Q (2) A, B and C (3) A, P, C and Q

(4) P, B and Q

Q. 6. The r.m.s. value of alternating current is 10 A, having frequency of 50 Hz. The time taken by the current to increase from zero to maximum and the maximum value of current will be (1) 2 × 10–2 sec and 14.14 A (2) 1 × 10–2 sec and 7.07 A (3) 5 × 10–3 sec and 7.07 A (4) 5 × 10–3 sec and 14.14 A Q. 7. In a Young's double slit experiment, the fringe width is found to be 0.4 mm. If the whole apparatus is immersed in water of 4 refractive index   , without disturbing 3 the geometrical arrangement, the new fringe width will be : (1) 0.30 mm (2) 0.40 mm (3) 0.53 mm

(4) 450 microns

202

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 8. A convex lens made of material of refractive index 1.5 and having a focal length of 10 cm is immersed in a liquid of refractive index 3.0. The lens will behave as (1) converging lens of focal length 10 cm

copper at 0°C, the temperature of interface is : (1) 80°C

(2) 20°C

(3) 60°C

(4) 40°C

(3) converging lens of focal length 10/3 cm

Q. 15. If the length of a cylinder on heating increases by 2%, the area of its base will increase by :

(4) diverging lens of focal length 30 cm.

(1) 0.5%

(2) 2%

Q. 9. dispersive power of crown glass? Given that mv  =  1.5230, mr = 1.5145

(3) 1%

(4) 4%

(2) diverging lens of focal length 10 cm

(1) 2°

(2) 3°

(3) 0.0163°

(4) 2.5°

Q. 10. An air bubble in glass slab (µ = 1.5) when viewed from one side, appears to be at 6 cm and from opposite side 4 cm. The thickness of glass slab is : (1) 10 cm

(2) 6.67 cm

(3) 15 cm

(4) None of these

Q. 11. A copper block of mass 2.5 kg is heated in a furnace to a temperature of 500°C and then placed on large ice block. The maximum amount of ice that can melt is (Specific heat of copper = 0.39 Jg–1 ° C–1, latent heat of fusion of water = 335 Jg–1) (1) 1.2 kg

(2) 1.455 kg

(3) 1 kg

(4) 2.5 kg

Q. 12. The number of molecules in 1   cm3 of an ideal gas at 0°C and at a pressure of 10–5 mm of mercury is : (1) 2.7 × 1011

(2) 3.5 × 1011

(3) 6.0 × 1023

(4) 6 × 1012

Pressure

Q. 13. In the figure shown here, the work done in the process ACBA is :

P0

C

(1) 40 m/s

(2) 80 m/s

(3) 20 m/s

(4) 100 m/s

Q. 17. If at same temperature and pressure, the densities for two diatomic gases are respectively d1 and d2, then the ratio of velocities of sound in these gases will be : d2 (1) d1

(2)

d1 d2

(3) d1d2

(4)

d1 d2

Q. 18. When a sound source of frequency n is approaching a stationary observer with velocity u than the apparent change in frequency is Dn1 and when the same source is receding with velocity u from the stationary observer than the apparent change in frequency is Dn2. Then (1) Dn1 = Dn2

A

3P 0

Q. 16. A long string, having a cross-sectional area 0.80 mm2 and density 12.5 g/cm3 is subjected to a tension of 64 N along the x-axis. One end of the string is attached to a vibrator moving in transverse direction. At t = 0, the source is at maximum displacement y = 1 cm. Find the speed of wave travelling on the string.

B

V 0 Volume 3V 0

(1) 4P0V0

(2) 6P0V0

(3) – 2P0V0

(4) – 4P0V0

Q. 14. A slab consist of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio 1 : 4. If the free face of brass is at 100°C and that of

(2) Dn1< Dn2

(3) Dn1 > Dn2

(4) Dn1 = Dn2 = 0

Q. 19. A wooden object floats in water kept in a beaker. The object is near a side of the beaker see (figure). Let P1, P2, P3 be the pressures at the three points A, B and C of the bottom as shown in the figure :

A

B

C

(1) P1 = P2 = P3

(2) P1 < P2 < P3

(3) P1 > P2 > P3

(4) P2 = P3 ≠ P1

203

MOCK TEST PAPER-4 Q. 20. A drop of water and a soap bubble have the same radii. Surface tension of soap solution is half of that of water. The ratio of excess pressure inside the drop and bubble is : (1) 1 : 2

(2) 2 : 1

(3) 1 : 4

(4) 1 : 1

Section B Q. 21. A capacitor of capacity 2  µF is charged to a potential difference of 12  V. It is then connected across an inductor of inductance 0.6 mH. The current in the circuit at a time when the potential difference across the capacitor is 6.0 V is ……× 10–1A. Q. 22. A 30 V storage battery is charged from 120 V direct current supply mains with a resistor being connected in series with battery to limit the charging current to 15 A. If all the heat produced in circuit, could be made available in heating water, the time it would take to bring 1 kg of water from 15°C to the 100°C is.......... minute [Neglect the internal resistance of the battery] Q. 23. Two conducting rails are connected to a source of emf and form an incline as shown in figure. A bar of mass 50 g slides without friction down the incline through a vertical magnetic field B. If the length of the bar is 50 cm and a current of 2.5 A is provided by battery. Value of B for which the bar slide at a constant velocity ……..×10–1 Tesla. 2 [g = 10 m/s ] B

R F Mg

θ θ

θ = 37°

Q. 24. A conductor ABOCD moves along its bisector with a velocity 1 m/s through a perpendicular magnetic field of 1 wb/m2, as shown in figure. If all the four sides are 1 m length each, then the induced emf between A and D in approx is …....... V.

× × O ×

B π/2 C

×

A ×

×

×

×

D ×

V=1m/s

Q. 25. A physical quantity A is dependent on other four physical quantities p, q, r and s as given below A =

pq

. The percentage r s error of measurement in p, q, r and s are 1%, 3%, 0.5% and 0.33% respectively, then the maximum percentage error in A is .......... %. Q. 26. A ball is thrown upwards from the foot of a tower. The ball crosses the top of tower twice after an interval of 4 seconds and the ball reaches ground after 8 seconds, then the height of tower is .......... m. (g = 10 m/s2) Q. 27. The minimum speed in m/s with which a projectile must be thrown from origin at ground so that it is able to pass through a point P (30 m, 40 m) is : (g = 10 m/s2) Q. 28. All the surfaces are frictionless. Strings are light and frictionless. The tension in string 1 is .......... N. (Take g = 10 m/s2) 1 kg

(2)

2 3

1/3kg

(1)

2 kg

Q. 29. A point P is located on the rim of wheel of radius r = 0.5 m which rolls without slipping along a horizontal surface then the total distance traversed by the point P in meters between two successive moments it touches the surface is .......... m. Q. 30. An over head tank of capacity 10 k litre is kept at the top of building 15 m high. Water falls in tank with speed 5 2 m/s. Water level is at a depth 5 m below ground. The tank is 1 to be filled in hr. If efficiency of pump is 2 67.5% electric power used is .......... W.

204

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Chemistry Section A Q. 31. A hydrated salt of Na2SO3 loses 22.22 % of its mass on strong heating. The hydrated salt is : (1) Na2SO3.4H2O

(2) Na2SO3.6H2O

(3) Na2SO3.H2O

(4) Na2SO3.2H2O

Q. 32. Which one of the following is the correct set with respect to molecule, hybridization and shape ? (1) BeCl2, sp2, linear

(2) BeCl2, sp2, triangular planar 2

(3) BCl3, sp , triangular planar (4) BCl3, sp3, tetrahedral CH3

Q. 33.

,

CH3 and

(1) BeO (2) BeCl2 (3) BeH2 (4) AlCl3 Q. 38. At 90°C pure water has [H3O+] = 10–6M. What is the value of Kw at this temperature? (1) 10–6 (2) 10–12 (3) 10–13 (4) 10–14 Q. 39. An equilibrium system for the reaction between hydrogen and iodine to give hydrogen iodide at 765K in a 5 litre volume contains 0.4 mole of hydrogen, 0.4 mole of iodine and 2.4 moles of hydrogen iodide. The equilibrium constant for the reaction is : H2 + I2 2HI, is (1) 36.0 (2) 15.0 (3) 0.067 (4) 0.028 Q. 40. In which of the following species O.N. of the element (s) is equal to + 4 ?

CH3

Number of secondary carbon atoms present in the above compounds are respectively :

(1) 6, 4, 5

(2) 4, 5, 6

(3) 5, 4, 6

(4) 6, 2, 1

Q. 34. Which type of isomerism can not be shown by benzaldoxime ?

(1) [N = C = S]

(2) H–O→H | H

NO+2 (3)

(4) C2H2

–

Q. 41. The order of stability of the following resonating structures

(2) Functional group isomerism

+

(3) 2I¯ + 2H + H2O2 → I2 + 2H2O (4) 2MnO4¯ + 6H+ + 5H2O2 → 2Mn2+ + 5O2 + 8H2O

⊕ ⊕

O

(4) Configuration isomerism

(2) PbS + 4H2O2 → PbSO4 + 4H2O

O

CH2 = CH– C – H (I), CH 2 – CH = C– H (II)

(3) Geometrical isomerism

(1) C6H6 + H2O2 → C6H5OH + H2O

⊕

O

(1) Optical isomerism

Q. 35. In which of the following reaction, H2O2 is behaving as a reducing agent :

+

Θ

and CH2 – CH = C – H (III) is :

(1) II > I > III (3) I > II > III

(2) I > III > II (4) III > II > I

NH4 Cl Q. 42. CH ≡ CH  product Cu4 Cl 2 →

Product is: (1) Cu–C ≡ C–Cu (3) CH=C–Cu

(2) CH2 ≡ CH–C ≡ CH (4) Cu–C ≡ C–NH4

Q. 36. Boric acid heated to red hot gives : (1) HBO2

(2) H2BO2

(3) B2O3

(4) Borax

High temperature → Y + CO; Q. 37. X + C + Cl2  of about 1000K

Y + 2H2O → Z + 2HCl

Compound Y is found in polymeric chain structure and is an electron deficient Molecule. Y must be :

+ CH2CH2CH2Cl

Q. 43.

AlCl3

(x)

CH3

hydrocarbon (X) major product X is :

(1)

CH2CH–CH2 CH3

205

MOCK TEST PAPER-4 (3) N-Methylchloramine

CH3 (2)

(4) Chloramine

C–CH3C

+

H / H2 O → Y  → Q. 49. X + 3NH3  H2N–CH2–COOH, compound X is :

CH3 (3)

(4)

CH2CH2CH2CH3

(1) Chloroacetic acid

CH3

(3) Both 1 and 2

CH–CH2CH3

(4) Acetic acid Q. 50. Nitrogen combines with metals to form :

(2) Bromoacetic acid

Q. 44. For CH3Br + OH – CH3OH + Br – the rate of reaction is given by the expression (1) rate = k [CH3Br] (2) rate = k [OH–] (3) rate = k [CH3Br] [OH–] (4) rate = k [CH3Br]0 [OH–]0 Q. 45. CH=CH2 CH2 CH3 OH

C

B CHCH3

A CH2 CH2 OH

OH

Select schemes A, B, C out of I acid catalysed hydration II  HBO III  oxymercuration-demercuration (1) I in all cases (2) I, II, III (3) II, III, I (4) III, I, II Q. 46. An aldehyde isomeric with allyl alcohol gives phenyl hydrazone. Pick out a ketone that too gives a phenyl hydrazone containing the same percentage of nitrogen : (1) Methyl ethyl ketone (2) Dimethyl ketone (3) 2–Butanone (4) 2–Methyl propanone Q. 47. The end product Y in the sequence of reaction : CN − NaOH → X  → Y is : RX  (1) An alkene (2) A carboxylic acid (3) Sodium salt of carboxylic acid (4) A ketone Q. 48. Methyl amine on reaction with chloroform in the presence of NaOH gives : (1) Methyl isocyanide (2) Methyl chloride

(1) Nitrites (2) Nitrates (3) Nitrosyl chlorides (4) Nitrides

Section B Q. 51. The specific rate constant of the decomposition of N2O5 is 0.008 min–1. The volume of O2 collected after 20 minutes is 16 ml. The volume that would be collected at the end of reaction is .......... mL. NO2 formed is dissolved in CCl4.

Q. 52. A sample of U238 (half life = 4.5 × 109 years) ore is found to contain 23.8 g of U238 and 20.6 g of Pb206. The age of the ore is .......... × 109 years. Q. 53. The equilibrium constant at 25°C for the given cell is .......... . Zn |Zn2+ (1M) || Ag+ (1M)| Ag is ..........1026. Given that



E0Zn/Zn2+ = 0.76 V

0 and E Ag/Ag+ = – 0.80 V

Q. 54. An ionic solid AB2 isomorphous to the rutile structure (a tetragonal system with effective number of formula units = 2) has edge lengths of the unit cell of 4Å, 4Å and 7Å. The density of the substance is .......... mg/cc. (if its formula weight is 80. Take NA = 6 × 1023 and express your answer in mg/cc using four significant digits.) Q. 55. 1000 g of 1 m sucrose solution in water is cooled to –3.534°C. What weight of ice would be separated out at this temperature is .......... gm. Kf (H2O) = 1.86K mol–1 Kg.) Q. 56. Coagulation value of the electrolytes AlCl3 and NaCl for As2S3 sol are 0.093 and 52 respectively. The No. of times AlCl3 has greater coagulating power than NaCl is .......... .

206

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 57. Total sodium ions which are present in one formula unit of sodium ethane-1, 2-diaminetetraacetatochromate (II) and sodium hexanitrito cobaltate (III) is .......... . Q. 58. In an ore of iron, iron is present in two oxidation state. Fen+ and Fe(n + 1)+ Number of Fe(n + 1)+ is twice the number of Fen+. If empirical formula of ore is FexO. The value of [x × 100] is .......... .

Q. 59. The wavelength in Å of the photon that is emitted when an electron in Bohr orbit with n = 2 returns to orbit with n = 1 in H atom is .......... Å. The ionisation potential of the ground state of H-atom is 2.17 × 10–11 erg. Q. 60. An element belonging to 3d series of modern periodic table has spin magnetic moment = 5.92 B.M. in +3 oxidation state. The atomic number of element is .......... .

Mathematics Section A Q. 61. If z1, z2 , z3 are complex numbers such that 1 1 1 + + = 1, then |z1| = |z2| = |z3| = z1 z 2 z 3 |z1 + z2 + z3| is : (1) equal to 1 (2) less than 1 (3) greater than 3 (4) equal to 3 Q. 62.

∫ ( log x )

2

dx equals :

(1) (x log x)2 – 2x log x + 2x + c (2) x (log x)2 – 2x log x + 2x + c (3) x (log x)2 + 2x log x + 2x + c (4) x (log x)2 + 2x log x – 2x + c Q. 63. Which one of the following is a fallacy (1) p ∨ (∼ q) ⇒ p ∧ q (2) ∼ [(p ∧ q)] ⇒ (∼ p ∨ q) (3) ∼ [(p ∨ ∼ q)] ⇒ p ∧ q (4) ∼ [(p ∧ ∼ q)] ⇒ p ∨ q Q. 64. The value of a for which the area between the curves y2 = 4ax and x2 = 4ay is 1 sq. unit, is : (1) (2) 4 3 3 (3) 4 3 (4) 4 Q. 65. The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is : (1) xy' = 2y (2) 2xy' = y (3) yy' = 2x (4) y" + y = 2x Q. 66. If the function y =

ax + b ( x − 4 )( x − 1) has an

extremum at P(2, –1), then the values of a and b are : (1) a = 0, b = 1 (2) a = 0, b = –1 (3) a = 1, b = 0 3

(4) a = –1, b = 0 2

Q. 67. If f (x) = x + 4x + lx + 1 (l ∈ R) is a monotonically decreasing function of x in the largest possible interval (–2, –2/3) then : (1) l= 4

(2) l = 2

(3) l = – 1

(4) l has no real value

d log x x = dx  2 log x  (1) x log x  x  (2) x log x (2 log x)

Q. 68.

 log x  log x (3) x log x  (log x)  (4) x  x  Q. 69. Number of values of x where the function  tan x log ( x − 2 ) ; x ∈ ( 2, 4 ) − {3, π}  2 f ( x )  x − 4 x + 3  1 tan x ; = x 3, π  6 is discontinuous, is .......... . (1) 2

(2) 1

(3) 0  x7  Q. 70. lim  x  x  2   

(4) Infinitely many x4

(1) e2 4

(3) e

(2) e3 (4) e5

Q. 71. If f (x) = x3 – 1 and domain of f = {0,1, 2, 3}, –1 then domain of f is : (1) {0, 1, 2, 3}

(2) {1, 0, –7, –26}

(3) {–1, 0, 7, 26}

(4) {0, –1,– 2, –3}

207

Mock Test Paper-4 Q. 72. The solution set of the inequation

log1/3 (x2 + x + 1) + 1 > 0 is :

(1) (–∞, –2) ∪ (1, + ∞) (2) [–1, 2] (3) (–2, 1) (4) (–∞, + ∞) Q. 73. The coefficient of y49 in

(y – 1) (y – 3) (y – 5) …… (y – 99) is .......... .

(1) 2500

(2) – 2500

(3) – 99 × 50

(4) 99 × 50

Q. 74. If α, β are roots of the equation x2 + px – q = 0 and γ, δ are roots of x2 + px + r = 0, then the value of (α – γ)(α – δ) is : (1) p + r

(2) p – r

(3) q – r

(4) q + r

Q. 75. If n AM’s are inserted between 1 and 31 and ratio of 7th and (n – 1)th A.M. is 5 : 9, then n equals : (1) 12

(2) 13

(3) 14

(4) 15

Q. 76. The line segment joining the points (1, 2) and (–2, 1) is divided by the line 3x + 4y = 7 in the ratio : (1) 3 : 4

(2) 4 : 3

(3) 9 : 4

(4) 4 : 9

Q. 80. The foci of a hyperbola coincide with the foci x2 y2 + = 1. Find the equation of the ellipse 25 9 of the hyperbola, if its eccentricity is 2. x2 y2 = 1 (1) 4 12

(2)

x2 y2 =2 4 12

x2 y2 = 1 (3) 9 45

(4)

x2 y2 =1 2 10

Section B Q. 81. Let ƒ(x) = sinx.cos3x and g(x) = cosx.sin3x, æ æpö æpö ö ç f ç ÷+ gç ÷ ÷ è7ø ÷ then the value of 7 ç è 7 ø ç æ 5p ö æ 5p ö ÷ ç g ç 14 ÷ + f ç 14 ÷ ÷ è øø è è ø is .......... . 2 2 2 2 Q. 82. Let y = sin θ + cos θ + tan θ + sec θ + 2 2 cosec θ + cot θ attains its least value (where q ∈ [0, 4p]), then number of such possible values of θ is .......... . Q. 83. In triangle ABC, a = 4, b = 3 and ∠A = 60°. If ‘c’ is a root of the equation c2 – 3c – k = 0. Then k = .......... . (with usual notations)

æ 1 - x2 ö -1 æ 2 x ö + cos-1 ç , Q. 84. If q = sin ç 2 ÷ 2 ÷ è1+ x ø è1+ x ø 3 for x ³ then the absolute value of 2

Q. 77. If the mean of the data 7, 7, 9, 7, 8, 7, l, 8 is 7, then the variance of this data is :

(1)

5 4

(2)

7 4

(3)

1 4

(4)

11 4

Q. 78. If the normal at the point (1, 2) on the parabola y2 = 4x meets the parabola again at the point (t2, 2t), then t is equal to (1) 1

(2) –1

(3) 3

(4) – 3

æ cos q + tan q + 4 ö ç ÷ is .......... . sec q è ø

Q. 85. If number of arrangements of letters of the word “DHARAMSHALA” taken all at a time so that no two alike letters appear together a b c d is (4 .5 .6 .7 ), (where a, b, c, d ∈ N), then a + b + c + d is equal to .......... . Q. 86. A five digit number is formed by the digits 1, 2, 3, 4, 5 without repetition. If the probability that the number formed is divisible by 4, is P, then 5P is .......... . 2 Q. 87. For f ( x ) = n x + x + 1 ,

Q. 79. An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the necessary length of the string and the distance between the pins respectively in cms, are :



g ( x ) = ( cos x )

then the value of

(2) 6,

(3) 4, 2 5

(4) 6 + 2 5 , 2 5

and

h( x ) =

ƒ(0)

ƒ( e )

ƒ( -e )

h(0)

ex - e-x , ex + e-x æpö gç ÷ è6ø h( p)

æ 5p ö g ç ÷ h( -p) ƒ(ƒ(ƒ(0))) è 6 ø

5

(1) 6, 2 5

( cos ecx -1)

is .......... .

208

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 88. The number of ordered pairs (a, b), (where a, b ∈ R) satisfying the equation a2008 + b2008 = 2008|a||b| – 2006 is equal to .......... . Q. 89. Let A(ˆi + 2 ˆj + 3kˆ), B( ˆj + kˆ) and C(3ˆi + 2 ˆj + 2 kˆ) are position vectors of vertices of ∆ABC and

4R2 the circumradius of ∆ABC is R then is 11 .......... . Q. 90. An edge of variable cube is increasing at the rate of 3 cm/s. The volume of the cube increasing fast when the edge is 10 cm long is .......... cm3/s.

Answers Physics Q. No.

Answer

1

(3)

2 3

Topic Name

Q. No.

Answer

Topic Name

Practical Physics

16

(2)

Transverse Waves

(3)

Photo Electric Effect

17

(1)

Sound Wave

(1)

Half Life

18

(3)

Doppler Effect

4

(2)

Atomic Structure & Matter Waves

19

(1)

Fluid Mech

5

(2)

Electrostatics

20

(4)

Properties of Matter

6

(4)

Alternating Current

21

6.00

Capacitance

7

(1)

Wave Nature of Light-Interference

22

4.4

Current Electricity

8

(2)

Refraction at Curved Surface

23

0.30

Megnate Field

9

(3)

Prism (Dispersion & Deviation)

24

1.414

Electromagnetic Induction

10

(3)

Refraction at plane surface

25

4.00

Unit & Dimension

11

(2)

Calorimetry

26

60.00

One Dimension

12

(2)

Kinetic Theory of Gases

27

30.00

Projectile Motion

13

(3)

Thermodynamics

28

8.00

Newton’s Law of Motion

14

(1)

Heat Transfer

29

4.00

Rotational Motion

15

(4)

Thermal expansion

30

843.75

WEP

Chemistry Q. No.

Answer

31

(4)

32 33

Topic Name

Q. No.

Answer

Topic Name

Mole Concept

46

(2)

Carbonyl Compound

(3)

Chemical Bonding

47

(3)

Carboxylic Acid

(1)

IUPAC

48

(3)

Nitrogen Compound

34

(2)

Isomerism

49

(3)

Biomolecules

35

(4)

Hydrogen and Its Compound

50

(4)

Nitrogen Family

36

(3)

P-Block (Boron)

51

17.49

Chemical Kinetics

37

(2)

s-Block Element

52

4.50

Nuclear Chemistry

38

(2)

Ionic Equilibrium

53

6.17

Electro-Chemistry

39

(1)

Chemical Equilibrium

54

2381

Solid State

40

(1)

Rodex Oxition

55

353

Solution

41

(3)

General Organic Chemistry

56

560

Surface Chemistry

42

(2)

Hydrocarbon

57

5.00

Coordination Compound

43

(4)

Aromatic Compound

58

75.00

Metallurgy

44

(3)

Halogen Derivative

59

1216

Atomic Structure

45

(3)

Alcohol, Ether and Phenol

60

26.00

Periodic Table

209

Mock Test Paper-4

Mathematics Q. No.

Answer

Q. No.

Answer

Topic Name

61

(1)

Complex Number

Topic Name

76

(4)

Straight Line

62

(2)

Indefinite Integration

77

(4)

Statistics

63

(2)

Mathematical Reasoning

78

(4)

Parabola

64

(4)

Area Under Curve

79

(4)

Ellipse

65

(1)

Differential Equation

80

(1)

Hyperbola

66

(3)

Maxima and Minima

81

7.00

Trigonometric Ratio

67

(1)

Monotonicity

82

8.00

Trigonometric Equation

68

(1)

Differentiation

83

7.00

Solutions to Triangle

69

(2)

Continuity

84

3.00

Inverse Trigonometric Functions

70

(4)

Limit

85

7.00

Permutation and Combination

71

(3)

Function

86

1.00

Probability

72

(3)

Logarithm

87

0.00

Determinants

73

(2)

Binomial Theorem

88

4.00

Matrix

74

(4)

Quadratic Equation

89

1.00

Vector

75

(3)

Progression

90

900

Tangent and Normal



5

MOCK TEST PAPER Time : 3 Hours

Total Marks : 300

General Instructions : 1. 2. 3. 4. 5. 6.

There are three subjects in the question paper consisting of Physics (Q. no. 1 to 30), Chemistry (Q. no. 31 to 60) and Mathematics (Q. no. 61 to 90). Each subject is divided into two sections. Section A consists of 20 multiple choice questions & Section B consists of 10 numerical value type questions. In Section B, candidates have to attempt any five questions out of 10. There will be only one correct choice in the given four choices in Section A. For each question 4 marks will be awarded for correct choice, 1 mark will be deducted for incorrect choice for Section A questions and zero mark will be awarded for not attempted question. For Section B questions, 4 marks will be awarded for correct answer and zero for unattempted and incorrect answer. Any textual, printed or written material, mobile phones, calculator etc. is not allowed for the students appearing for the test. All calculations / written work should be done in the rough sheet is provided with Question Paper.

Physics Section A Q. 1. If energy (E), velocity (V) and force (F), be taken as fundamental quantities, then what are the dimensions of mass ? (1) EV2

(2) EV–2

–1

–2

(3) FV

(4) FV

(3)

2 v ( n − 1) n v ( n + 1) n





(2) (4)

v ( n − 1) n



n

Q. 3. Work done in converting one gram of ice at –10°C into steam at 100°C is : (2) 6056 J

(3) 721 J

(4) 616 J

(2) Increased by 200 J (4) Decreased by 200 J

2v ( n + 1)

(1) 3045 J

(1) Increased by 400 J (3) Increased by 100 J

Q. 2. A body starts from rest with constant acceleration a, its velocity after n second is v. The displacement of body in last two seconds is : (1)

Q. 5. A gas is compressed at a constant pressure of 50 N/m2 from a volume of 10 m3 to a volume of 4 m3. Energy of 100 J is then added to the gas by heating. Its internal energy is :

Q. 4. Which of the following quantities is zero on an average for the molecules of an ideal gas in equilibrium ? (1) Kinetic energy

(2) Momentum

(3) Density

(4) Speed

Q. 6. Two rectangular blocks A and B of different metals have same length and same area of cross-section. They are kept in such a way that their cross-sectional area touch each other. The temperature at one end of A is 100°C and that of B at the other end is 0°C. If the ratio of their thermal conductivity is 1 : 3, then under steady state, the temperature of the junction in contact will be : (1) 25°C

(2) 50°C

(3) 75°C

(4) 100°C

Q. 7. An anisotropic material has coefficient of linear thermal expansion a1, a2 and a3 along x, y and z–axis respectively. Coefficient of cubical expansion of its material will be equal to : (1) a1 + a2 + a3

(2) a1 + 2a2 + 3a3 α + α2 + α3 (3) 3a1 + 2a2 + a3 (4) 1 3

211

MOCK TEST PAPER-5 Q. 8. Two strings A and B, made of same material are stretched by same tension. The radius of string A is double of the radius of B. A transverse wave travels on A with speed vA v and on B with speed vB. The ratio A is : vA 1 (1) (2) 2 2

1 (4) 4 4 Q. 9. In the interference of two sources of intensities I0 and 9I0 the intensity at a point π where the phase difference is is : 2 (1) 10 I0 (2) 8 I0 (3)

(3)

82 I0

(4) 4 I0

Q. 10. When an engine passes near to a stationary observer then its apparent frequencies occurs in the ratio 5/3. If the velocity of engine is : (1) 540 m/s

(2) 270 m/s

(3) 85 m/s

(4) 52.5 m/s

Q. 11. The value of series limit in the case of paschen series is : (1) 1875 nm

(2) 122 nm

(3) 822 nm

(4) tending to zero

Q. 12. Two radioactive sources A and B of half lives of 1 hour and 2 hours, respectively, initially contain the same number of radioactive atoms. At the end of two hours, their rates of disintegration are in the ratio of : (1) 1 : 4

(2) 1 : 3

(3) 1 : 2

(4) 1 : 1

Q. 13. If the frequency of light in a photoelectric experiment is doubled, the stopping potential will : (1) be doubled (2) be halved (3) become more than double (4) become less than double Q. 14. The dependence of g on geographical latitude at sea level is given by

g = g0(1 + b sin2f) where f is the latitude angle and b is a dimensionless constant. If Dg is the error in the measurement of g then the error in measurement of latitude angle is :

(2) Df =

(1) zero (3) Df =

∆g g 0 β sin ( 2φ )

∆g ∆g (4) Df = g 0 β cos ( 2φ ) g0

Q. 15. A point object is placed at a distance of 30 cm from a convex mirror of focal length 30 cm. What is the separation between the image and the object? (1) 40 cm (2) 45 cm (3) 50 cm (4) 55 cm Q. 16. A glass slab of thickness 4 cm contains the same number of waves as 5 cm of water. When both are traversed by the same monochromatic light. If the refractive index 4 of water is   . What is that of glass ? 3 5 5 (1) (2) 4 3

16 (4) 1.5 15 Q. 17. The maximum value of index of refraction of a material of a prism which allows the passage of light through it when the refracting angle of the prism is A is : (3)

(1)

A 1 + sin   2

(2)

A 1 + cos   2

(3)

A 1 + tan 2   2

(4)

A 1 + cot 2   2

Q. 18. A convex lens of focal length 15 cm is placed coaxially in front of a convex mirror. The lens is 5 cm from the pole of the mirror. When an object is placed on the axis at a distance of 20 cm from the lens, it is found that the image coincides with the object. Calculate the radius of curvature of the mirror - (consider all optical event) : (1) 45 cm (2) 55 cm (3) 65 cm (4) 85 cm Q. 19. In the diagram shown, the separation between the slit is equal to 3l, where l is the wavelength of the light incident on the plane of the slits. A thin film of thickness 3l and refractive index 2 has been placed in the front of the upper slit. The distance of the central maxima on the screen from O is:

212

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

S1 O S2

D

(1) D (3)

(2)

λD d

λd D

(4) None of these

Q. 20. In a hydraulic press there is a larger piston of diameter 35 cm at a height of 1.5 m relative to the smaller piston of diameter 10 cm. A 20 kg mass is loaded on the smaller piston. Density of oil in the press is 750 kg/m3. The thrust on the load by the larger piston is :

1.5 m

20 kg

(1) 1.1 × 103 N

(2) 1.3 × 103 N

(3) 1.1 × 104 N

(4) 1.3 × 104 N

Q. 23. A ball of mass m = 20 kg released from height h = 10 m falls on the Earth’s surface. The speed of the Earth when the ball reaches on the Earth’s surface is ............ × 10–23 m/s. Q. 24. A solid sphere, rolls on a rough horizontal surface with a linear speed 7 m/s collides elastically with a fixed smooth vertical wall. Then the speed of the sphere, when it has started pure rolling in the backward direction is ............ m/s. Q. 25. An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. If the satellite is stopped in its orbit and allowed to fall freely onto the earth, the speed with which it hits the surface ............ km/s. [g = 9.8 ms–2 and Re = 6400 km] Q. 26. A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible string of length 20 cm, fixed at its mid point. The bob is displaced slightly, perpendicular to the plane of the rod and string. The period of small oscillations of the πx system in the form is ............ sec. and 10 value of x is ............. (g = 10 m/s2)  = 20 cm

Section B Q. 21. A wet open umbrella is held upright and is rotated about the handle at a uniform rate of 21 revolutions in 44 s. If the rim of the umbrella is circle of 1 metre in diameter and the height of the rim above the floor is 1.5 m, the drops of water spun off the rim and hit the floor at a horizontal .......... m from umbrella. Q. 22. A block of mass 2.0 kg is pulled up on a smooth incline of angle 30° with the horizontal. If the block moves with an acceleration of 1.0 m/s2, the power delivered by the pulling force at a time 4.0 s after the motion starts is ............ J/s.

A





Bob

Q. 27. A non-conducting sphere of radius R = 5 cm has its centre at origin O of co-ordinate system. It has a spherical cavity of radius r = 1 cm having its centre at (0, 3 cm). Solid material of sphere has uniform positive 10 −6 charge density r = coulomb m–3. The π potential at point P is ............volt. (4 cm, 0). Q. 28. Two identical capacitors are connected as shown and having initial charge Q0. Separation between plates of each capacitor is d0. Suddenly the left plate of upper capacitor and right plate of lower capacitor

213

MOCK TEST PAPER-5 start moving with speed v towards left while other plate of each capacitor remains fixed. QV (given 0 = 10 A). The value of current in 2d0 the circuit is………. A. V

minimum number of 100 watt light bulb operated at 120 volts in home is ............. Q. 30. A charged particle is accelerated through a potential difference of 12 kV and

Q0

acquires a speed of 106 m s–1. It is projected perpendicularly into the magnetic field of Q0

strength 0.2 T. The radius of circle described

V

is…………… cm.

Q. 29. A 15 A circuit breaker trips in home when the current through it, reaches 15 A. The

Chemistry Section A Q. 31. The correct IUPAC name of 2-ethyl-3pentyne is : (1) 3-methyl hexyne-4 (2) 4-ethyl pentyne-2 (3) 4-methyl hex-2-yne (4) None of these Q. 32. How many conformations does ethane have? (1) 1 (2) 2 (3) 3 (4) Infinite Q. 33. H2O2 can be obtained when following reacts with H2SO4 except with (1) PbO2 (2) BaO2 (3) Na2O2 (4) SrO2 Q. 34. Which of the following compounds are formed when boron trichloride is treated with water. (1) H3BO3 + HCl (2) B2H6 + HCl (3) B2O3 + HCl (4) None of these ∆ ,205° C ∆ ,120° C Q. 35. Y ←  CaSO4.2H2O  → X. X and Y are respectively (1) plaster of paris, dead burnt plaster (2) dead burnt plaster, plaster of paris (3) CaO and plaster of paris (4) plaster of paris, mixture of gases

Q. 36. The acceptable resonating structures of the following molecule are : ..

..O CH 3––CH CH==CC––..O .. –CH2 – CH 3 CH 3 – CH = .. –CH2 – CH 3 | O CH C – 3 .. –CH2 – CH 3 | |:N :N :N CH 3 3C CH HH3C C 3 H 3 Θ CH 3

Θ.. 

..

(x) CH3 –..Θ..C H – C –....O CH2––CH CH 3 (x) CH H – C||–O O.. –CH CH3––C 2 3 (x) – C||–⊕.... –– CH CH 3 2 – CH 3 || ⊕ NN⊕ N



CH3 3C CH HH3C C 3 CH H 3Θ .. ⊕3 Θ .. ⊕ Θ (y) O CH3 –..CCHH –CC== ⊕ .. – CH2 – CH3 (y) CH O .. – CH2 – CH3 |=O (y) CH33 –– C H –– C .. – CH2 – CH3 | |:N :N :N CH3 3C CH HH3C C 3 CH H 3⊕ .. 3 .. ⊕ (z) CH3 –⊕ CH2––CH CH3 .. O (z) CH CCHH –CC||––O O.. –CH 2 3 (z) CH33 ––C H –– C – .... –– CH 2 – CH3 | | ||NΘΘ NΘ N CH3 3C CH HH3C C 3 CH H Θ 3 3⊕ ⊕ Θ (w) CH3 –⊕ –CH CH2––CH CH3 Θ (w) CCH HH––CC|== CH3––C OO–– CH 2 3 (w) CH – C| =O 3 2 – CH3 :N | :N :N CH 3 3C CH HH3C C 3 CH H 3 3

(1) x, y (3) y, z

(2) x, z (4) z, w

214

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 37. What would be the product when ethene is oxidised with cold dil. KMnO4 solution : (Hydrocarbon) CH 2–CH2 | OH OH

(1) |

(2)

H – C – OH (3) || O

H– C – H || O

(1) CH3CH2CH2OH (2) CH3 −CH−CH3 | OH (3) CH3OCH2CH3

(4) CH3CH2CHO

Q. 42. Benzoic acid gives benzene on being heated with X and phenol gives benzene on being heated with Y. Therefore X and Y are respectively

(4) CO2 + H2O

Q. 38.

(1) Soda lime and copper (2) Zinc dust and sodium hydroxide



 → C6H5 – X Functional groups Y, –CH = CH2 and X respectively are ... and ... directing. ozonolysis

(3) Zinc dust and soda lime (4) Soda lime and zinc dust

(2) Meta, meta and meta

Q. 43. Alkylamine dissolve in hydrochloric acid to form alkylammonium chloride. The nitrogen in the latter salt is :

(3) Meta, ortho–para and meta

(1) Quadricovalent only

(4) All the three ortho–para

(2) Tricovalent only

(1) Meta, ortho–para and ortho–para

Q. 39. Isocyanide reaction involves intermediate formation of (1) : CCl2

(2) +CH3

(3) : CH3–

(4) : CCl3–

NaBH 4 Q. 40. B ←

CH = CH–CHO

the

H 2 /Pt  → A



A and B are -

(1)

CH2CH2CHO, CH=CH–CH2OH CH2CH2CH2OH,



CH=CH–CH2OH

(4)

CH=CH–CH2OH in both cases CH2CH2CH2OH in both cases

[ ] → C 3H 6 O Q. 41. C3H8O  K 2 Cr2 O7 /H 2 SO4 O



(4) Quadricovalent, Unielectrovalent Q. 44. Two elements X (atomic weight = 75) and Y (atomic weight = 16) combine to give a compound having 75.8% X. The formula of the compound is : (1) XY

(2) X2Y

(3) X2Y2

(4) X2Y3

Q. 45. In the reaction–(Biomolecules)

(2)

(3)

(3) Unielectrovalent only

I2 + NaOH ( aq.)  → CHI3,

In this reaction the first compound is :



[X] → nCH2–CH=CH2



Reagent X is :

—CH — CH2 — CH3

n

(1) Triethylaluminiumandtitanium tetrachloride (2) Triethyl aluminium (3) Zeigler Natta Catalyst (4) both 1 and 3 Q. 46. On heating Cu(NO3)2 strongly, the material finally obtained is : (1) Cu

(2) Cu2O

(3) Cu(NO2)2

(4) Cu(NO3)2

(1) Blue

(2) Green

(3) Yellow

(4) Orange

Q. 47. The value of D0 for RhCl63– is 243 KJ/mol what wavelength of light will promote an electron from. The colour of the complex is :

215

MOCK TEST PAPER-5 Q. 48. Gold is extracted by making soluble cyanide complex. The cyanide complex is : –

(1) [Au(CN)4]

(3) [Au(CN)3]–

(2) [Au(CN)2]

–

(4) [Au(CN)]–



Q. 49. A white powder when strongly heated gives off brown fumes. A solution of this powder gives a yellow precipitate with a solution of KI. When a solution of barium chloride is added to a solution of powder, a white precipitate results. This white powder may be : (1) A soluble sulphate (2) KBr or NaBr

monolayer on the surface of iron catalyst is 8.15 ml/g of the adsorbent. if each nitrogen molecule occupies 16 × 10–22 m2. The surface area of the 100 g adsorbent will be .......... × 1018 m2. Q. 56. A solution of a non volatile solute in water freezes at –0.30°C. The vapour pressure of pure water at 298 K is 23.51 mm Hg and Kf for water is 1 – 86 degree/mol. The vapour pressure of rain solution at 298 K is .......... mm Hg. Q. 57. A jar contains a gas and a few drops of water

(3) Ba(NO3)2

Q. 55. Volume of N2 at NTP required to form a

at T K. The pressure in the jar is 830 mm of

(4) AgNO3

Q. 50. In which of the following species S atom assumes sp3 hybrid state ?

Hg. The temperature of the jar is reduced



temperatures are 30 and 25 mm of Hg. The

(I) (SO3);    (II) SO2,   (III) H2S   (IV) S8

(1) I, II

(2) II, III

(3) II, IV

(4) III, IV

Section B Q. 51. A definite volume of H2O2 undergoing spontaneous decomposition required 22.8 c.c. of standard permanganate solution for titration. After 10 and 20 minutes respectively the volumes of permanganate required were 13.8 and 8.25 c.c. The time required for the decomposition to be half completed is .......... min. Q. 52. The half-life of cobalt 60 is 5.26 years. The percentage activity remaining after 4 years is ............%. Q. 53. The e.m.f. of cell Zn | ZnSO4 || CuSO4| Cu at 25°C is 0.03 V and the temperature coefficient of e.m.f. is –1.4 × 10–4 V per degree. The heat of reaction for the change taking place inside the cell is – (.............) kJ/ mol. Q. 54. If NaCl is doped with 10-3 mol % of SrCl2. The concentration of cation vacancy is ............ × 1018.

by 1%. The vapour pressure of water at two new pressure in the jar is ............ mm of Hg. Q. 58. The molar heats of formation of NH4NO3 (s) is – 367.54 kJ and those of N2O (g), H2O (l) are 81.46 and – 285.8 kJ respectively at 25°C and atmosphere pressure. The difference of ∆H and ∆E of the reaction NH4NO3 (s) → N2O (g) + 2H2O(l) is ........ kJ. Q. 59. A 0.5 g sample of an iron-containing mineral mainly in the form of CuFeS2 was reduced suitably to convert all the ferric iron into ferrous form and was obtained as a solution. In the absence of any interfering matter, the solution required 42 ml of 0.01 M K2Cr2O7 solution

for

titration.

The

percentage

of CuFeS2 in the mineral is ..........% (Cu = 63.5, Fe = 55.8, S = 32, O = 16). Q. 60. Sulphide ion in alkaline solution reacts with solid sulphur to form polysulphide ions having formula , S 22 − , S 32 − , S 24 − , etc. if K1 = 2−

12 for S+S2-  S 2 and K2 = 132 for 2S+S2 S 32 − , K3 = ............ for S + S 22 −  S 32 −

216

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Mathematics Section A   1 Q. 61.  log ( log x ) +  dx = 2 ∫ ( log x )   x +c (1) x log log x + log x

(2) x log log x + 2 x + c log x (3) x log log x − x + c log x 2x (4) x log log x − +c log x 4 6 2n 2   1  n2  2 2  n2  3 2  n2  n 2  n2   lim 1 1 1 ... 1 + + + +         Q. 62. n →∞  n 2  n2   n2  n2         is equal to :

e 4

4 e e (3) 1 (4) 2 Q. 63. If (a, b), (c, d) are points on the curve 9y2 = x3 (1)

(2)

where the normal makes equal intercepts on the axes, then the value of a + b + c + d is : (1) 0

(2) 8

(3) 27

(4) 64

Q. 64. Let f(x) be a function such that ;

f ' (x) = log1/3 (log3(sin x + a)) (where a ∈ R). If f(x) is decreasing for all real values of x then the exhaustive solution set of a is .......... .

(1) (1, 4)

(2) (4, ∞)

(3) (2, 3)

(4) (2, ∞)

Q. 65. If ( 3 + i )( z + z ) − ( 2 + i )( z − z ) + 14i = 0, then z z is equal to : (1) 10

(2) 8

(3) –9

(4) –10

Q. 66. The length of the perpendicular from the point (2, –1, 4) on the straight line, x+3 y−2 z = = is : 10 −7 1 (1) greater than 3 but less than 4 (2) less than 2 (3) greater than 2 but less than 3 (4) greater than 4

 Q. 67. The vector p perpendicular to the vectors   a = 2ˆi + 3ˆj − k and b =ˆi − 2 ˆj + 3k and satisfy-

(

)

 ing the condition p ⋅ 2ˆi − ˆj + kˆ = –6 is :

(

(2) 3 −ˆi + ˆj + kˆ

(1) −ˆi + ˆj + kˆ

(

)

(3) 2 −ˆi + ˆj + kˆ

)

(4) ˆi − ˆj + kˆ

Q. 68. If a2 + b2 + c2 = – 2 and

(1 + b ) x (1 + c ) x ) x 1 + b x (1 + c ) x ) x (1 + b ) x (1 + c ) x

1 + a2 x

( (1 + a

f (x ) = 1 + a2 2

2

2

2

2

2

2

then f (x) is a polynomial of degree (1) 1 (2) 0 (3) 3 (4) 2 Q. 69. If ax4 + bx3 + cx2 + dx + e = 2x x −1 x +1 x + 1 x 2 − x x − 1 , then the value of e, is :

x −1 x +1 3x (1) 0 (2) –2 (3) 3 (4) –1 Q. 70. Number of integral values of x satisfying the 6 x + 10 − x 2

27 3 inequality   is : < 4 64   (1) 6 (2) 7 (3) 8 (4) Infinite Q. 71. If α and β are the roots of the equation 1 1 2 and are the roots of x + px + 2 = 0 and β α 1  the equation 2x2 + 2qx + 1 = 0, then  α −  α   1  1  1  β −   α +   β +  is equal to : β β α       9 9 9 + q2 (2) 9 − q2 4 4 9 9 (3) 9 + p2 (4) 9 − p2 4 4 Q. 72. The sum of the series 1.32 + 2.52 + 3.72+.... upto 20 terms is : (1) 188090 (2) 180890 (3) 189820 (4) 180889 Q. 73. If mC3 + mC4 > m + 1C3, then least value of m is : (1) 6 (2) 7 (3) 5 (4) 4 (1)

(

)

(

)

(

)

(

)

217

MOCK TEST PAPER-5 Q. 74. Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.

Q. 79. (x – 1) + (y – 2) = 13 represents hyperbola whose eccentricity is :

(1) 69762

(2) 69676

(1)

(3) 69760

(4) 69766

Q. 75. If m1 and m2 are roots of the equation

(

) (

)

x 2 + 3 + 2 x + 3 − 1 = 0 then the area of the triangle formed by the lines y = m1x, y = m2x and y = c is :

 33 − 11  2  33 + 11  2 (1)   c (2)   c 4 4    

 33 + 11  2  33 − 11  2  c (4)   c (3)  2 2     Q. 76. If the length of the chord of the circle, x2 + 2 2 y = r (r > 0) along the line, y –2x = 3 is r, 2 then r is equal to :

(1)

9 5

12 (4) 5

Q. 77. The centre of the circle passing through the 2 point (0, 1) and touching the parabola y = x at the point (2, 4) is :

 − 53 16  ,  (1)  10 5  

 6 53  (2)  ,   5 10 



 3 16  (3)  ,   10 5 

 − 16 53  ,  (4)  5 10  

Q. 78. The eccentricity, foci and the length of the 2 2 latus rectum of the ellipse x + 4y + 8y – 2x + 1 = 0 are respectively equal to :

(2)

(3)

2

(

)

3 ; 1 ± 3, −1 ; 2 2

(

)

3 ; 1 ± 3, 1 ; 1 2

(

)

3 ; 1 ± 3, −1 ; 1 2

(

)

3 ; 1 ± 3, 1 ; 2 (4) 2

3 ( 2x + 3 y + 2 )

13 3

2

13 3

(2)

(3)

(4) 3 3 Q. 80. If the point (1, 3) serves as the point of 3 2 inflection of the curve y = ax + bx then the value of ‘a’ and ‘b’ are (1) a =

3 3 and b = – 2 2

3 9 and b = 2 2 3 9 (3) a = –  and b = – 2 2 (2) a =

3 9 (4) a = –  and b = 2 2

Section B

(2) 12

24 (3) 5

(1)

2

5π   f ( x= ) 3 cos  x + − 5 sin x + 2 6  

Q. 81. If

then

maximum value of ƒ(x) is .......... = Q. 82. Let x

sin 3 θ cos3 θ , = y and cos2 θ sin 2 θ

p 1 where p and q sin θ + cos θ = . If x + y = q 2 are coprime then (p + q) is equal to : ..........

Q. 83. Consider ƒ(x) = sin–1[2x] + cos–1([x] –1) (where [.] denotes greatest integer function.) If domain of ƒ(x) is [a, b) and the range of ƒ(x) 2d is equal to .......... is {c, d} then a + b + c (where c < d) Q. 84. If 0 < x < π and cos x + sin x =



(1)

(1 − 7 )

4

(



)

(2)

1 , then tan x is 2

(4 − 7 )

3

(

)

4+ 7 1+ 7 (3) − (4) 3 4 Q. 85. Let a real valued function ƒ(x) satisfying ƒ(x + y) + ƒ(x – y) = ƒ(x)ƒ(y) {ƒ(0) ≠ 0} " x, y ∈ R, then ƒ(–2) – ƒ(–1) + ƒ(0) + ƒ(1) – ƒ(2) is equal to ..........

218

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 86. The value of lim x ®0

(sin( ne x ))2 ( e tan

2

- 1)

x

is ..........

Q. 87. P(x) be a polynomial satisfying P(x) – 2P’(x) 3 2 = 3x – 27x + 38x + 1. If function ì P ''( x ) + 18 ïï 6 f (x) = í 1 ïsin ( ab ) + cos-1 ( a + b - 3ab ), ïî

p 2

x¹ x=

p 2

p is continuous at x = , then (a + b) is equal 2 to .......... . (sin x ) Q. 88 If y = x to .......... .

¥ x x(sin x )

, then

p dy at x = is equal 2 dx

Q. 89. If y = ƒ(x), ƒ '(0) = ƒ(0) = 1 and if y = ƒ(x) d 2 y dy satisfies 2 + = x , then the value of [ƒ(1)] dx dx is .......... (where [.] denotes greatest integer function) Q. 90. A man has 3 pairs of white socks and 2 pairs of blue socks kept together in a bag. If he dressed up hurriedly in the dark, the probability that after he has put on a white sock, he will then put on another white M M sock is ( is in simplest form) then n n n – M = .......... .

Answers Physics Q. No.

Answer

1

(2)

2 3

Topic Name

Q. No.

Answer

Topic Name

Unit & Dimension

16

(1)

Refraction at plane surface

(1)

One Dimension

17

(4)

Prism

(3)

Calorimetry

18

(2)

Refraction at Curve Surface

4

(2)

Kinetic Theory of Gases

19

(1)

Wave Optics

5

(1)

Thermodynamics

20

(2)

6

(1)

Heat Transfer

21

0.829

Circular Motion

7

(1)

Thermal Expansion

22

48.00

Rotational Motion

8

(1)

Transverse Wave

23

4.66

Conservation Law

Fluid Mech

9

(1)

Sound Wave

24

3.00

Rotational Motion

10

(3)

Dopplar Effect

25

7.919

Gravitation

11

(3)

Atomic Structure & Matter wave

26

4.00

Elasticity

12

(3)

Nuclear Physics & Radioactivity

27

35.16

Current Electricity

13

(3)

Photo Electric Effect

28

20.00

Capacitance

14

(2)

Practical Physics

29

18.00

Current Electricity

15

(2)

Reflection at Plane and Curve Surface

30

12.00

Magnetic Effect of Current

Q. No.

Answer

Chemistry Q. No.

Answer

Topic Name

Topic Name

31

(3)

IUPAC

46

(2)

Transition Elements

32

(4)

Isomerism

47

(4)

Coordination compound

33

(1)

Hydrogen & Its Compound

48

(2)

Metallurgy

34

(1)

p-Block(Boron)

49

(4)

Salt Analysis

35

(1)

(s-Block)

50

(4)

Oxygen Family

36

(1)

General Organic Chemistry

51

13.71

Chemical Kinetic

37

(1)

Hydrocarbon

52

53.00

Nuclear Chemistry

38

(3)

Aromatic Compound

53

13.842

Electrochemistry

219

Mock Test Paper-5 39

(1)

Halogen Dervitative

54

6.02

Solid State

40

(2)

Salt Analysis

55

35.00

Surface Chemistry

41

(2)

Carbonyl Compound

56

23.44

Solution

42

(4)

Carboxylic Acid

57

817.00

Gaseous States

43

(4)

Nitrogen Compound

58

2.324

Chemical Energetics

44

(4)

Practical Chemistry

59

92.40

Redox Reaction

45

(4)

Biomolecules

60

11.00

Chemical Equilibrium

Mathematics Q. No.

Answer

61

(3)

62

(2)

63

Topic Name

Q. No.

Answer

Topic Name

Indefinite Integration

76

(1)

Circle

Definite Integration

77

(4)

Parabola

(2)

Tangent and Normal

78

(3)

Ellipse

64

(2)

Monotonicity

79

(3)

Hyperbola

65

(1)

Complex Number

80

(4)

Maxima and Minima

66

(2)

Three Dimensional Plane

81

9.00

Trigonometric Ratio

67

(2)

Vector

82

97.00

Trigonometric Equation

68

(3)

Metrics

83

4.00

Inverse Trigonometric Functions

69

(1)

Determinants

84

330

Trigonometry

70

(2)

Logarithm

85

2.00

Function

71

(4)

Quadratic Equation

86

1.00

Limit

72

(1)

Progression

87

2.00

Continuity

73

(2)

Binomial Therom

88

1.00

Differentiation

74

(3)

Permutation and Combination

89

1.00

Differential Equation

75

(2)

Straight Line and Point

90

4.00

Probability



6

MOCK TEST PAPER Time : 3 Hours

Total Marks : 300

General Instructions : 1. 2. 3. 4. 5. 6.

There are three subjects in the question paper consisting of Physics (Q. no. 1 to 30), Chemistry (Q. no. 31 to 60) and Mathematics (Q. no. 61 to 90). Each subject is divided into two sections. Section A consists of 20 multiple choice questions & Section B consists of 10 numerical value type questions. In Section B, candidates have to attempt any five questions out of 10. There will be only one correct choice in the given four choices in Section A. For each question 4 marks will be awarded for correct choice, 1 mark will be deducted for incorrect choice for Section A questions and zero mark will be awarded for not attempted question. For Section B questions, 4 marks will be awarded for correct answer and zero for unattempted and incorrect answer. Any textual, printed or written material, mobile phones, calculator etc. is not allowed for the students appearing for the test. All calculations / written work should be done in the rough sheet is provided with Question Paper.

Physics Section A Q. 1. A displacement vector, at an angle of 30° with y-axis has an x-component of 10 units. Then the magnitude of the vector is : (1) 5.0 (2) 10 (3) 11.5 (4) 20 1 = ut − at 2 where S is the Q. 2. The formula S 3 distance travelled, u is the initial velocity, a is the acceleration and t is the time is : (1) only dimensionally correct (2) dimensionally incorrect (3) dimensionally and numerically correct (4) dimensionally and numerically wrong Q. 3. A stone is dropped from the top of the tower and travels 24.5 m in the last second of its journey. The height of the tower is :  (g = 9⋅8 m/s2) (1) 44.1 m (2) 49 m (3) 78.4 m (4) 72 m Q. 4. Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If p the angle of projection of one is and its 3 maximum height is y1 then the maximum height of the other will be :

(1) 3y1

(2) 2y1

y1 y (4) 1 2 3 Q. 5. The masses of 10 kg and 20 kg, respectively, are connected by massless spring as shown in the figure. A force of 200 N acts on the 20 kg mass. At the instant shown, the 10 kg mass has acceleration of 12 m/s2. What is the acceleration of 20 kg mass ? (g = 10 m/s2) (3)

10 kg

20 kg 200 N

(1) 12 m/s2 (2) 4 m/s2 (3) 10 m/s2 (4) zero Q. 6. Block A has a mass of 2 kg and block B has 20 kg. If the coefficient of kinetic friction between block B and the horizontal surface is 0.1, and B is accelerating towards the right with a = 2 m/s2, then the mass of the block C will be : (g = 10 m/s2)

(1) 15 kg (3) 5.7 kg

(2) 12.5 kg (4) 10.5 kg

221

MOCK TEST PAPER-6 Q. 7. The specific heat of a substance is given by C = a + bT, where a = 1.12 kJ kg–1K–1 and b = 0.016 kJ–kg K–2. The amount of heat required to raise the temperature of 1.2 kg of the material from 280 K to 312 K is : (1) 205 kJ

(2) 215 kJ

(3) 225 kJ

(4) 235 kJ

Q. 8. In a cubical box of volume V, there are N molecules of a gas moving randomly. If m is mass of each molecule and v2 is the mean square of x component of the velocity of molecules, then the pressure of the gas is : 1 mNv 2 3 V

(2) P =

mNv 2 V

1 (4) P = mNv2 mNv 2 3 Q. 9. An ideal gas is taken through series of changes ABCA. The amount of work involved in the cycle is : (3) P =

P 4P1 P1

(1)

M2

a a , 3 11

(2)

a a , 3 4

(4)

a a , 6 2

a a , 12 4 Q. 12. A cylindrical vessel of diameter 12 cm contains 800p cm3 of water. A cylindrical glass piece of diameter 8.0 cm and height 8.0 cm is placed in the vessel. If the bottom of the vessel under the glass piece is seen by the paraxial rays (see figure), locate its image from bottom. The index of refraction of glass is 1.50 and that of water is 1.33. (3)

A

C V1

B 3V1 V

(1) 12P1V1

(2) 6P1V1

(3) 3P1V1

(4) P1V1

Q. 10. A thin square steel plate with each side equal to 10 cm is heated by a blacksmith. The rate of radiated energy by the heated plate is 1134 watts. The temperature of the hot steel plate is :

M1

8 cm

(1) P =

2R

(Stefan's constant s = 5.67 × 10–8 watt m–2K–4 emissivity of the plate = 1)

(1) 570 K

(2) 1189 K

(3) 2500 K

(4) 750 K

Q. 11. Two spherical mirrors, one convex and the other concave, each of same radius of curvature R are arranged coaxially at a distance of 2R from each other. A small circle of radius a is drawn on the convex mirror as shown in figure. What is the radii of first two images of the circle?

8 cm 12 cm

(1) 2.1 cm

(2) 7.1 cm

(3) 9.1 cm

(4) 11.1 cm

Q. 13. A prism of refractive index 2 and refracting angle A produces minimum deviation dm of a ray on one face at an angle of incidence 45°, The values of A and dm are, respectively, (1) 45°, 45° (2) 45°, 60° (3) 60°, 30° (4) 60°, 45° Q. 14. A converging lens of focal length f is placed at a distance 0.3 m from an object to produce an image on a screen 0.9 m from the lens. With the object and the screen in the same positions, an image of the object could also be produced on the screen by placing a converging lens of focal length (1) f at a distance 0.1 m from the screen (2) f at a distance 0.3 m from the screen (3) 3 f at a distance 0.3 m from the screen (4) 3 f at a distance 0.1 m from the screen

222

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 15. Monochromatic green light of wavelength 5 × 10–7 m illuminates a pair of slits 1 mm apart. The separation of bright lines in the interference pattern formed on a screen 2 m away is : (1) 0.25 mm (2) 0.1 mm (3) 1.0 mm (4) 0.01 mm Q. 16. What is the electric potential needed to excite He+ to its first excited state? (1) 40.8 V (2) 20.4 V (3) 10.2 V (4) 81.6 V Q. 17. The activity of a certain radionuclide decreases to 15 percent of its original value in 10 days. What is its half life? [ln (0.15) = –1.9]. (1) 3.00 days (2) 3.50 days (3) 3.65 days (4) 3.8 days Q. 18. When ultraviolet light of wavelength 100 nm is incident upon a sample of silver metal, a potential difference of 7.7 volt is required to stop the photoelectrons from reaching the collector plate. The potential required to stop photo electrons when light of wavelength 200 nm is incident upon silver is : (1) 1.5 V (2) 1.85 V (3) 1.95 V (4) 2.37 V Q. 19. A vernier calliper has 20 divisions on the vernier scale, which coincide with 19 on the main scale. The least count of the instrument is 0.1 mm. The main scale divisions are of : (1) 0.5 mm (2) 1 mm (3) 2 mm (4) 1/4 mm Q. 20. A racing car moving towards a cliff sounds its horn. The sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If V is the velocity of sound, the velocity of the car is : V V (1) (2) 2 2 (3)

V 3

(4)

V 4

Q. 22. The greatest speed of transverse waves through a steel wire of radius 1 mm is .......... × 102 m. The breaking stress of steel is 6.0 × 108 Nm–2. Density of steel = 7800 kg m–3. Q. 23. Length of steel rod so that it is 5 cm longer than the copper rod at all temperatures should be .......... cm.

(a for copper = 1.7 × 10–5 / °C and a for steel = 1.1 × 10–5 / °C)

Q. 24. An inclined plane makes an angle of 30° with the horizontal electric field E of 100 V/m. A particle of mass 1 kg and charge 0.01 C slides down from a height of 1 m. If the coefficient of friction is 0.2, the time taken for the particle to reach the bottom is .......... sec. E = 100 V/m 1m 30°

Q. 25. A capacitor filled partially with dielectric material of dielectric constant 'k'. Its electric potential versus position graph is as shown. Distance between the two plates is 4 mm. The dielectric constant of medium is .......... . Potential (in volts) 10 4 3 2

3

4

x (in mm)

Q. 26. One solenoid is centered inside another. The outer one has a length of 50.0 cm and

Section B

contains 6750 coils, while the coaxial inner

Q. 21. An engine is approaching a cliff at a constant speed. When it is at a distance of 0.9 km from cliff it sounds a whistle. The echo of the sound is heard by the driver after 5 seconds. Velocity of sound in air is equal to 330 ms–1. The speed of the engine is .......... km/h

solenoid is 3.0 cm long and p cm2 in area and contains 150 coils. The current in the outer solenoid is changing at 3000 A/s. The emf induced in the inner solenoid is .......... V. (Round off to two decimal places.)

223

Mock Test Paper-6 Q. 27. Total momentum of electrons in a straight wire of length L carrying a current I is P, if mass of electron is doubled keeping its charge constant, and length of the wire is also doubled keeping current constant. the new value of momentum will be nP. so the value of n will be .......... . –5 Q. 28. A particle of mass 5 × 10 kg is placed at the lowest point of a smooth parabola having the equation 20 x2 = y (x, y in m). Here y is the vertical height. If it is displaced slightly and it is constrained to move along the parabola, the angular frequency (in rad/s) of small oscillations is .......... .

Q. 29. In the widest part of the horizontal pipe oil is flowing at a rate of 2 m/sec. The speed (in m/s) of the flow of oil in the narrow part of the tube if the pressure difference in the broad and narrow parts of the pipe is 0.25 roil g, is .......... m/s. 2

Q. 30. A coil of effective area 4 m is placed at right angles to the magnetic induction B. The e.m.f. of 0.32 V is induced in the coil. When the field is reduced to 20% of its initial value in 0.5 sec. Find B (in wb/m2).

Chemistry Section A

Q. 35. Stannous chloride solution when kept in air turns milky due to the formation of :

Q. 31. Write the IUPAC name of the compound CH3CH2– C – C – CH3

(1) Sn(OH)2

(2) Sn(OH)Cl

(3) Sn(OH)4

(4) SnCl4

CH2CH2 (1) 3-ethyl-2-methyl butadiene-1,3 (2) 2-ethyl-3-methyl butadiene-1,3 (3) 2-ethyl-4-methyl butadiene-1,2 (4) 2-ethyl-4-methyl butadiene-2,3 Q. 32. Acetamide is isomer of : NH2

Q. 36. The compound sprinkled on road to keep them wet and prevent dust from flying is : (1) Calcium hydroxide (2) Calcium chloride (3) Calcium sulphate (4) Calcium hydride

(1) 1-amino ethanol CH3 – CH–OH

Q. 37. The most stable free radical among the following is :

(2) Formamide H–C–H

(1) C6H5CH2C H2

O

(3) Ethyl amine C2H5NH2 (4) Acetaldehyde oxime CH3–CH=N–OH Q. 33. H2O2 → H2O + O2 This represents : (1) Oxidation of H2O2 (2) Reduction of H2O2 (3) Disproportionation of H2O2 (4) Acidic nature of H2O2 Q. 34. In diborane : (1) 2 bridged hydrogen and four terminal hydrogen are present (2) 3 bridged and three terminal hydrogen are present (3) 4 bridged hydrogen and two terminal hydrogen are present (4)  1 bridged hydrogen and 1 terminal hydrogen are present

•



•

(3) C6H5C HCH3

•

(2) CH3–C H–CH3

•

(4) CH3C H2

Q. 38. What would be the main product when propene reacts with HBr : HH HH | | | | (2) CH3 –C–C–H (1) CH3 –C–C–H | | | | Br H H Br (3) Both a and B (4) Br–CH2–CH=CH2 AlCl 3 + CH2Cl2 ¾¾¾ ® A, A is :

Q. 39. (excess)

CH2Cl

CHCl2

(1)



(3)

CH2

(2)

(4)

224

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 40. What would be the product when neopentyl chloride reacts with sodium ethoxide : (1) 2-Methyl-butan-2-ol (2) Neo pentyl alcohol (3) Both A and B (4) 2-Methyl-but-2-ene Q. 41. The missing structures A and B in the reaction sequence: Al 2 O3 → R–CH=CH2 R–CH2–CH2OH  350° C



(i) O3 Reduce  → RCHO + A; RCHO → B; (ii) ZnH3 O⊕ are :

(1) CH3OH, RCOOH (2) Methanal, RCH2OH (3) Ethanal, RCOOH (4) Methanal, RCHOHR Dil → Product. Q. 42. CH3–CH2–CHO  alkali product in the above reaction is : (1) CH3–CH2COOH (2) CH3–CH2–CH2OH (3) CH3–CH2–CH– CH2– CHO | OH

The

CH3 | (4) CH –CH –CH– CH– CHO 3 2 | OH Q. 43. Identify the product A in the following reaction ∆ COOH  → CH COOH + A CH2 3 COOH (1) CO2 (2) CH3CHO (3) CH3OH (4) None of these Q. 44. When propionamide reacts with Br2 in the presence of alkali the product is : (1) CH3CH2CH2NH2 (2) CH3CH2NH2 (3) C3H7CN (4) C2H5CN Q. 45. A pyranose ring consists of a skeleton of : (A) 5 carbon atoms and one oxygen atom (2) 6 carbon atoms (3) 6 carbon atoms and one oxygen atom (4) 4 carbon atoms and one oxygen atom Q. 46. A mixture of benzene and chloroform is separated by : (1) Sublimation

(2) Separating funnel

(3) Crystallization (4) Distillation

Q. 47. Which of the following is a double salt : (1) Carnallite (2) Mohr’s salt (3) Alum (4) All are correct Q. 48. Heating of MgCl2 6H2O in absence of HCl gives : (1) MgCl2 (2) MgO (3) Mg3N2 (4) Mg(OH)2 Q. 49. A reddish-pink substance on heating gives off a vapour which condenses on the sides of the test tube and the substance turns blue. If on cooling water is added to the residue it turns to original colour. The substance is : (1) Iodine crystals (2) Copper sulphate crystals (3) Cobalt chloride crystals (4) ZnO Q. 50. Ozone on reacting with KI in neutral medium produces : (1) KIO3 (2) KOH (3) KCl (4) KO2

Section B Q. 51. The decomposition of N2O into N2 and O2 in presence of gaseous argon follows second order kinetics, with 29000 K − k = (5.0 × 1011 L mol-1 s-1) e T . Arrhenius parameters are .......... kJ mol–1. Q. 52. The total number of a and b particles

Q. 53.

Q. 54.

Q. 55.

Q. 56.

238 214 U → 82 Pb emitted in the nuclear reaction 92 is.......... . The solubility of Co2[Fe(CN)6)] in water at 25°C from the following data : Conductivity of saturated solution of Co2[Fe(CN)6] = 2.06 × 10–6 ohm–1 cm–1 and that of water = 4.1 × 10–7 ohm–1 cm–1. The ionic molar conductivities of Co2+ and [Fe(CN)6]4– are 86 and 444 ohm–1 cm2 mol–1 respectively, is .......... × 10–6 mol/L. In an ionic solid r(+) = 1.6 Å and r(–) = 1.864 Å. Use the radius ratio rule to the edge length of the cubic unit cell is .......... Å. A storage battery contains a solution of H2SO4 38% by weight. At this concentration, vant Hoff factor is 2.50. At the battery content freeze temperature will be .......... K. Kf = 1.86 K Kg mol-1. The density of gold is 19 g/cm3. If 1.9 × 10–4 g of gold is dispersed in one litre of water to

225

MOCK TEST PAPER-6 give a sol having spherical gold particles of radius 10 nm, the number of gold particles per mm3 of the sol will be .......... × 106. Q. 57. A given mixture consists only of pure substance X and pure substance Y. The total weight of the mixture is 3.72 gm. The total number of moles is 0.06. If the weight of one mole Y is 48 g\d and if there is 0.02 mole X in the mixture, the weight of one mole of X is .......... g. Q. 58. The number of times larger the spacing between the energy levels with n = 3 and n = 8 spacing between the energy level with

n = 8 and n = 9 for the hydrogen atom is .......... . Q. 59. Dipole moment of HX is 2.59 x 10-30 coulomb-metre. Bond length of HX is 1.39  Å. The ionic character of molecule is .......... %. Q. 60. For the gaseous reaction, K(g) + F(g) → K+(g) + F–(g), ∆H was calculated to be 19 kcal/mol under conditions where the cations and anions were prevented by electrostatic separation from combining with each other. The ionisation energy of K is 4.3 eV. The electron affinity of F is .......... . (in eV)

Mathematics Section A Q. 61.

∫ 2x

3x + 1 dx equals : − 2x + 3

2

(1)

1 5  2x − 1  log 2 x 2 − 2 x + 3 − tan −1  +C 4 2  5 

(2)

3 5  2x − 1  log 2 x 2 − 2 x + 3 + tan −1  +C 4 2  5 

(3)

3 5  4x − 2  log 2 x 2 − 2 x + 3 + tan −1  +C 4 2 5  

( (

(

) )

)

(4) 1 log 2 x 2 − 2 x + 3 − 5 tan −1  4 x − 2  + C 4 2  5 

(

p

Q. 62.

x sin x

∫ 1 + cos 0

2

x

)

dx equals :

p 4 p2 p2 (3) (4) 4 2 Q. 63. Area in first quadrant bounded by y = 4x2, x = 0, y = 1 and y = 4 is : 5 3 (1) (2) 7 7 (1) 0

(3)

7 3

(2)

(4)

7 5

Q. 64. If the curves y2 = 6x, 9x2 + by2 = 16, cut each other at right angles then the value of b is : (1) 2 (2) 4 (3)

9 2

(4) 3

Q. 65. Let f(x) = tan–1 f(x), where f(x) is p monotonically increasing for 0 < x < . 2 Then f (x) is : p  (1) increasing in  0,  2  p  (2) decreasing in  0,  2   (3) increasing in  0,  p p , 4 2    (4) decreasing in  0,  p p 4, 2   Q. 66. The function g ( x ) =

p and decreasing in 4  p and increasing in 4  f (x) x

, x ≠ 0 has an

extreme value when : (1) g' (x) = f(x) (2) f (x) = 0 (3) x g' (x) = f(x) (4) g (x) = f ' (x) Q. 67. The ratio

2

log

21/ 4

a

−3

(

log 27 a 2 + 1

) − 2a simplifies to 3

7 4 log 49 a − a − 1 (1) a – a – 1 (2) a2 + a – 1 2

(3) a2 – a + 1 (4) a2 + a + 1 Q. 68. The number of real solutions of 1 1 x− 2 = 2− 2 is : x −4 x −4 (1) 0 (2) 1 (3) 2 (4) infinite Q. 69. A GP consists of an even number of terms. If the sum of all the terms is 5 times the

226

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

sum of the terms occupying odd places, the common ratio will be equal to : (1) 2 (2) 3 (3) 4 (4) 5 Q. 70. If sum of the coefficient of second and

5 1 fourth terms in the expansion of  2 x − 2  ,



3x 

in descending powers of x, is S, Then The 81 S of is : 40 (1) 27 (2) 57 (3) 72 (4) 75 Q. 71. If the vertices of a triangle be (0, 0), (6, 0) and (6, 8), then its incentre will be : (1) (2, 1) (2) (1, 2) (3) (4, 2) (4) (2, 4) Q. 72. If the line 3x + 4y = m touches the circle x2 + y2 = 10x, then m is equal to : (1) – 40, 10 (2) 40, – 10 (3) 40, 10 (4) –40, –10 Q. 73. Which of the following are not parametric coordinates of any point on the parabola y2 = 4ax : 2a (1) (at2, 2at) (2)  am 2 ,  m  value

(3) (a/m2, 2a/m) (4) (am2, –2am) Q. 74. Tangents are drawn from a point on the circle x2 + y2 = 25 to the ellipse 9x2 + 16y2 – 144 = 0 then find the angle between the tangents. 3p p (1) (2) 4 4 p 2p (3) (4) 2 3 Q. 75. Parametric form of the hyperbola x2 y2 − = – 1 is : 4 9 (1) (2 tan q, 3 sec q) (2) (3 sec q, 2tan q) (3) (9 sec q, 4 tan q) (4) (3 tan q, 2 sec q) Q. 76. Consider Statement 1 : (p∧∼q) ∧ (∼ p ∧ q) is a fallacy. Statement 2 : (p → q) ↔ (∼ q → ∼ p) is a tautology. (1) Statement- 1 is true; Statement- 2 is true; Statement- 2 is a correct explanation for Statement- 1 (2) Statement- 1 is true; Statement- 2 is true; Statement- 2 is not a correct explanation for Statement- 1 (3) Statement- 1 is true; Statement- 2 is false. (4) Statement- 1 is false; Statement- 2 is true

Q. 77. If 1, a1, a2,..... an–1 are the roots of unity, then (1 + a1) (1 + a2) .......(1 + an–1) is equal to (when n is even) : (1) n – 1 (2) n (3) 0 (4) 2 Q. 78. The d.c's of a line whose direction ratios are 2, 3, –6, are : −2 3 −6 2 3 −6 (1) , , (2) , , 7 7 7 7 7 7 2 −3 −6 −2 −3 −6 , (3) , (4) , , 7 7 7 7 7 7 Q. 79. Unit vector perpendicular to the plane ofthe   triangle ABC with position vectors a , b , c of the vertices A, B, C is :       a×b + b ×c + c ×a (1) ∆       a×b + b ×c + c ×a (2) 2∆       a×b + b ×c + c ×a (3) 4∆ 2 a×b + b×c + c×a (4) ∆ Q. 80. The minimum number of zeros in an upper triangular matrix will be : n ( n − 1) n ( n + 1) (1) (2) 2 2 2n ( n − 1) (3) (4) None of these 2

(

)

(

)

(

)

(

)

Section B 3 Q. 81. The Probability that A speaks truth is 4 4 and that of B is . The probability that 5 they contradict each other in stating the same fact is p, then the value of 40p is : Q. 82. Let right angled isosceles triangle ABC be inscribed in a circle according to adjacent diagram vertex A is moved along the circle ' = pr , if to reach at A’ such that are AA 3 2 = r 3 + 1 then (A’C) is ........... A

A’ B

r

C

Q. 83. Let l1,l2 ∈[0, p] are the solutions of the p  p  equation cosec  + x  + cosec  − x  = 2 2, 4 4     then 8(sin2 l1 + sin2 l2) is equal to ..........

227

Mock Test Paper-6 Q. 84 Let x = sin–1(sin  8) + cos–1(cos  11) + tan–1(tan  7), and x = k (π – 2⋅4) for an integer k, then the value of k is......... Q. 85. If in a frequency distribution, the mean and madian are 21 and 22 respectively, then its mode is approximately .......... Q. 86. Number of selections of at least one letter from the letters of MATHEMATICS, is .......... Q. 87. Let (p1, q1, r1) & (p2, q2, r2) are satisfying 1 p p2 1 q q 2 = 6 (where pi, qi, ri ∈ N and pi < 1 r r2 qi < ri and i = 1, 2) and point (p1, q1, r1) lies on the plane 2x + 3y + 6z = k1 and point (p2, q2, r2) lies on the plane 2x+3y + 6z = k2 (where p1= p2= 1) If distance between these planes is ‘d’, then value of (210d) is .......... .

ì1 ü x-2 ì1 ü Q. 88. Let f : R - í ý → R - í ý , f ( x ) = 2 x -1 î2 þ 2 î þ be a function such that x = m is the solution of ƒ(x) + 2ƒ –1(x) + 2 = ƒ(ƒ(x)), then m is equal to .......... . Q. 89. The value of lim

(sin( ne x ))2

x ®0

( e tan

2

x

- 1)

is .......... .

Q. 90. If functions g & h are defined as ìïx 2 + 1 g( x ) = í 2 ïî px

x ÎQ xÎQ

x ÎQ ì px and h( x ) = í x + q x ÎQ 2 î If (g + h)(x) is continuous at x = 1 and x = 3, then 3p + q is .......... .



Answers Physics Q. No.

Answer

1

(4)

Topic Name Vector

Q. No.

Answer

16

(1)

Topic Name Atomic Structure & Matter Wave

2

(1)

Unit & Dimension

17

(3)

Nuclear Physics and Radioactivity

3

(1)

One Dimension

18

(1)

Photo Electric Effect

4

(4)

Projectile

19

(3)

Practical Physics

5

(2)

Newton’s Law of Motion

20

(2)

Doppler Effect

6

(4)

Friction

21

108

Sound Wave

7

(3)

Calorimetry

22

8

(2)

Kinetic Theory of Gases

23

14.17

Thermal Expansion

9

(3)

Thermodynamics

24

2.00

Electrostatics

10

(2)

Heat Transfer

25

3.00

Capacitance

11

(1)

Reflection at Plane and Curve Surface

26

2.43

Electromagnetic Induction

12

(2)

Refraction at Plane Surface

27

4.00

Current Electricity

13

(3)

Prism

28

20.00

Simple Harmonic Motion

14

(2)

Refraction at Curve Surface

29

3.00

Fluid Mech

15

(3)

Wave Nature of Light-Interference

30

0.05

Electromagnetic induction

[2.77 or 2.78 or 2.76]

Transverse Wave

Chemistry Q. No.

Answer

31

(2)

32

Topic Name

Q. No.

Answer

Topic Name

IPUAC

46

(4)

Practical Organic Chemistry

(4)

Isomerism

47

(4)

Coordination compound

33

(3)

Hydrogen Family

48

(2)

Metallurgy

34

(1)

p- Block (Boron Family)

49

(3)

Salt Anaylise

35

(2)

p-Block (Carbon Family)

50

(2)

Oxygen Family

228

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

36

(2)

s-Block

51

241.10

Chemical kinetics

37

(3)

General Organic Chemistry

52

8.00

Nuclear Chemistry

38

(1)

Hydrocarbon

53

2.67

Electrochemistry

39

(3)

Aromatic Compound

54

4.00

Solid

40

(4)

Halogen Dervitative

55

243.92

41

(2)

Alcohol, Ether & Phenol

56

2.40

Surface Chemistry

42

(4)

Carbonyl Compound

57

90.00

Mole Concept

43

(1)

Carboxylic Acid

58

3.23

Atomic Structure

44

(2)

Nitrogen Compound

59

11.65

Chemical Bonding

45

(1)

Biomolecules

60

3.48

Periodic Table

Solution

Mathematics Q. No.

Answer

61

(2)

62

(3)

63

Topic Name

Q. No.

Answer

Topic Name

Indefinite Integration

76

(2)

Mathematical Reasoning

Definite Integration

77

(3)

Complex Numbers

(3)

Area Under Curve

78

(1)

Three dimensional Plane

64

(3)

Tangent and Normal

79

(2)

Vectors

65

(1)

Monotonicity

80

(1)

Matrices

66

(4)

Maxima & Minima

81

14.00

Probability

67

(4)

Logarithm

82

2.00

Circles

68

(1)

Quadratic Equations

83

6.00

Trigonometric Equations

69

(3)

Progressions

84

5.00

Inverse Trigonometric Functions

70

(2)

Binomial Theorem

85

24

71

(3)

Straight Line & Point

86

863.00

Permutation and Combination

72

(2)

Circle

87

90.00

Determinants

73

(2)

Parabola

88

2.00

Functions

74

(3)

Ellipse

89

1.00

Limits

75

(1)

Hyperbola

90

2.00

Continuity

Statistics



MOCK TEST PAPER Time : 3 Hours

7 Total Marks : 300

General Instructions : 1. 2. 3. 4. 5. 6.

There are three subjects in the question paper consisting of Physics (Q. no. 1 to 30), Chemistry (Q. no. 31 to 60) and Mathematics (Q. no. 61 to 90). Each subject is divided into two sections. Section A consists of 20 multiple choice questions & Section B consists of 10 numerical value type questions. In Section B, candidates have to attempt any five questions out of 10. There will be only one correct choice in the given four choices in Section A. For each question 4 marks will be awarded for correct choice, 1 mark will be deducted for incorrect choice for Section A questions and zero mark will be awarded for not attempted question. For Section B questions, 4 marks will be awarded for correct answer and zero for unattempted and incorrect answer. Any textual, printed or written material, mobile phones, calculator etc. is not allowed for the students appearing for the test. All calculations / written work should be done in the rough sheet is provided with Question Paper.

Physics Section A Q. 1. The tube AC forms a quarter circle in a vertical plane. The ball B has an area of crosssection slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will : A

N B

mg cos 

mg C

(1) always be in contact with the inner wall of the tube

(2)  always be in contact with the outer wall of the tube

(3) initially be in contact with the inner wall and later with the outer wall

A

v

B C

v 2 (2)  A comes to rest and (B + C) moves with v velocity 2 (3) A moves with velocity v and (B + C) moves with velocity v (4)  A and B come to rest and C moves with velocity v Q. 4. A rod of mass ‘M’ & length ‘L’ lying on a frictionless horizontal surface is initially given an angular velocity ‘w’ about vertical axis with centre of mass at rest but circular motion is not fixed. Subsequently end A of rod collides with nail P, which is near to A such that end A becomes stationary immediately after impact. Velocity of end ‘B’ just after collision will be : (1) All the three balls move with velocity

 

interval of time covering the same distance, is. (1) twice (2) four times (3) three times (4) same Q. 3. As shown in figure A, B and C are identical balls B and C are at rest and, the ball A moving with velocity v collides elastically with ball B, then after collision :

(4)  initially be in contact with the outer wall and later with the inner wall

Q. 2. Energy required to accelerate a car from 10 to 20 m s–1 compared with that required to accelerate from 0 to 10 ms–1 in the same

230

Oswaal JEE (Main) Mock Test 15 Sample Question Papers B



P



(1) wL wL 4

A

(2)

wL 2

7 wL 3 Q. 5. If R is the radius of the earth and g the acceleration due to gravity on the earth’s surface, the mean density of the earth is :

(3)

(1)

4 pG 3 gR

(4)

(2)

3pR 4 gG

3g (3) 4 pRG

pRg (4) 12G Q. 6. A particle is oscillating according to the equation X = 7cos 0.5 pt, where t is in second. The point moves from the position of equilibrium to maximum displacement in time : (1) 4.0 second (2) 2 second (3) 1.0 second (4) 0.5 second Q. 7. A ball falling in a lake of 200 m shows a decrease of 0.1 % in its volume at the base of the lake. The bulk modulus of elasticity of the material of the ball is (take g = 10 m/s2) : (1) 109 N/m2 (2) 2 × 109 N/m2 9 2 (3) 3 × 10 N/m (4) 4 × 109 N/m2 Q. 8. In a capillary tube, water rises to a height of 4 cm. If the cross-sectional area of the tube were one-fourth, water would have risen to a height of : (1) 2 cm (2) 4 cm (3) 8 cm (4) 16 cm Q. 9. What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one half that of a freely falling body? (The densities of metal and of liquid are r and s respectively and the viscosity coefficient of the liquid is h) (1)

r2 g (r – 2s) 9h

(2)

r2 g (2r – s) 9h

(3)

r2 g (r – s) 9h

(4)

2r 2 g (r – s) 9h

Q. 10. A solid cone of height 25 cm and base diameter 25 cm floats in water with its vertex downwards such that 20 cm of its axis is immersed. The additional weight that must be placed at the centre of the base such that the cone now is completely immersed in water is : (1) 1 kg

(2) 2 kg

(3) 3 kg

(4) 4 kg

Q. 11. The electric field in a certain region is  given by E = (5ˆi - 3ˆj ) kV/m. The potential difference VB – VA between points A and B, having coordinates (4, 0, 3)m and (10, 3, 0)m respectively, is equal to (1) 21 kV

(2) –21 kV

(3) 39 kV

(4) –39 kV

Q. 12. A child is standing in front of a straight plane mirror. His father is standing behind him, as shown in the fig.

H



H

The height of the father is double the height of the child. What is the minimum length of the mirror required so that the child can completely see his own image and his father’s image in the mirror? Given that the height of father is 2H.

H 2 3H (3) 2 (1)

(2)

5H 6

(4) None

Q. 13. If the refracting angle of a prism is 60° and minimum deviation is 30°, the angle of incidence is : (1) 30°

(2) 45°

(3) 60°

(4) 90°

Q. 14. The wave front of a light beam is given by the equation x + 2y + 3z = C, (where C is arbitrary constant) then the angle made by the direction of light with the y¯axis is :

231

MOCK TEST PAPER-7 (1) cos–1

1 14

(3) cos–1

14 3

(4) sin–1



Section B

2

(2) sin–1



14 14 Q. 15. A film projector magnifies a 100 cm2 film strip on a screen. In such a way that the distance between the screen and the projector is divided in the ratio of 2:1 by the lens. Then the area of magnified film on screen is : (1) 1600 cm2 (2) 400 cm2 2 (3) 800 cm (4) 200 cm2 Q. 16. What are the number of wave lengths that can be emitted by hydrogen atoms when an electron falls from the fifth orbit to its ground state? (1) 4 (2) 5 (3) 10 (4) 3 Q. 17. If the short series limit of the Balmer series for hydrogen is 3646 Å. Calculate the atomic no. of the element which gives X-ray wavelength down to 1.0 Å. Identify the element : (1) z = 21 (2) z = 31 (3) z = 11 (4) z = 5 Q. 18. The wavelength of a neutron with energy 1 eV is closest to : (1) 10–2 cm (2) 10–4 cm –6 (3) 10 cm (4) 10–8 cm Q. 19. A photoelectric experiment is performed at two different light intensities I1 and I2 (>I1). Choose the correct graph showing the variation of stopping potential versus frequency of light. I2 I 1 (1) I2 I (2)

f1

(3)

V

1

V

V

O f0

f

f1 I1

O

Q. 21. The lengths of sides of cuboid are a, 2a and 3a. If the relative percentage error in the measurement of a is 1%, then the relative percentage error in the measurement of volume of cube is .......... %. Q. 22. In the figure shown, the velocity of lift is 2 m/s while string is winding on the motor shaft with velocity 2 m/s and block A is moving downwards with a velocity of 2 m/s, the velocity of block B .......... m/s. 2 m/s

A

B 2 m/s

Q. 23. Figure shows the graph of the x-co-ordinate of a particle going along the x-axis as function of time. Then, the instantaneous speed of particle at t = 12.5 s is .......... m/s. x

A

8m 4m

f0

f

O

4s

8s

12 s

16 s B

(4) None of these

I2

f

Q. 20. If a semiconductor has an intrinsic carrier concentration of 1.41 × 1016 m–3, when doped with 1021 m–3 phosphorus, then the concentration of holes at room temperature will be : (1) 2 × 1021 (2) 2 × 1011 (3) 1.41 × 1010 (4) 1.41 × 1016

Q. 24. A projectile is fixed at an angle 60° with horizontal. Ratio of initial K.E. to K.E when velocity vector of projectile makes an angle 15° with velocity of projection is .......... . Q. 25. Three blocks A, B and C of mass m each are arranged in pulley mass system as shown. Coefficient of friction between block A and horizontal surface is equal to 0.5 and a force P acts on ‘A’ in the direction shown. The value of P/mg so that block ‘C’ doesn’t move is :

232

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

P

A

C

B

Q. 26. On an X temperature scale, water freezes at –125°X and boils at 375°X. On a Y temperature scale water freezes at –70°Y and boils at –30°Y. The value of temperature on X-scale equal to the temperature of 50°Y on Y-scale is ..............°X. Q. 27. A parallel plate capacitor is maintained at a certain potential difference. When a 3 mm thick slab is introduced between the plates, in order to maintain the same potential difference the distance between the plates is increased by 2.4 mm. The dielectric constant of slab is .......... . Q. 28. Power dissipated by the circuit is ......... W. 3 R

Q. 29. There is a constant homogeneous electric field of 100 Vm–1 within the region x = 0 and x = 0.167 m pointing in the positive x-direction. There is a constant homogeneous magnetic field B within the region x = 0.167 m and x = 0.334 m pointing in the z-direction. A proton at rest at the origin (x = 0, y = 0) is released in the positive x-direction. The minimum strength of the magnetic field B, so that the proton will come back at x = 0, y = 0.167 m (mass of the proton = 1.67 × 10–27 kg) is...........mT. Q. 30. A plane loop is shaped in the form as shown in figure with radii a = 20 cm and b = 10 cm and is placed in a uniform time varying magnetic field B = B0 sin wt, where B0 = 10 mT and w = 100 rad/s. The amplitude of the current induced in the loop is ..... A, if its resistance per unit length is equal to 50 × 10–3 Ω/m. The inductance of the loop is negligible.

1 2

Q 12V

×

× ×

× ×

×

× ×

×

× × b × ×

× ×

4 6

× × a

× ×

×

×

× × B×

×

8

P

5

4

Chemistry Section A Q. 31. The

name

of

ClCH2 – C

C – CH2 Cl

Br Br according to IUPAC nomenclature system is (1) 2,3-dibromo-1,4-dichlorobut-2-ene (2) 1,4-dichloro-2,3-dibromobut-2-ene (3) dichlorobromobutene (4) dichlorobromobutane Q. 32. Only two isomeric monochloro derivatives are possible for (excluding stereo) (1) n-butane (2) 2,2-dimethylpentane

(3) benzene (4) neopentane Q. 33. D2O (heavy water) and H2O differ in the following except (1) Freezing point (2) Density (3) Ionic product of water (4) Its reaction with sodium Q. 34. The type(s) of bonds present in diborane is/ are : (1) Covalent (2) One centre bond (3) Covalent and three centre bond (4) Covalent and one centre bond

233

MOCK TEST PAPER-7 Q. 35. When CO is heated with NaOH under pressure, we get (1) Sodium benzoate (2) Sodium acetate (3) Sodium formate (4) Sodium oxalate Q. 36. The following compounds have been arranged in order of their increasing thermal stabilities. Identify the correct order. K2CO3(I), MgCO3(II), CaCO3 (III), BeCO3 (IV) (1) I < II < III < IV (2) IV < II < III < I (3) IV < II < I < III (4) II < IV < III < I Q. 37. The heat of hydrogenation of benzene is 51 kcal/mol and its resonance energy is 36 kcal/mol. What will be the heat of hydrogenation of cyclohexene ? (1) 18 kcal mol–1 (2) 29 kcal mol–1 (3) 50 kcal mol–1 (4) 26 kcal mol–1 Q. 38. Cl | CH3 – CH –CH3

Na/ether  

A (major product).

A is : (1) CH3 – CH2 – CH2 – CH2 – CH2 – CH3 (2) CH3–CH–CH–CH3 | | CH3 CH3 (3) No reaction (4) CH3 – CH = CH2 CH COCl

Zn–Hg 3 → A  → B Q. 39. C6H6  AlCl 3

HCl

The end product in the above sequence is : (1) Toluene (2) Ethyl benzene (3) Both the above (4) None I2 → → (A)  Q. 40. CH3–C–CH3  Ag Powder

Na2 CO3

||

O



H SO

2 4 → (C). Product A, B and C are : (B)  ++

Hg

(1) Iodoform, Acetylene and Acetaldehyde (2) Tri. iodomethane, Ethyne and Acetone (3) Iodoform, Ethene and Ethylene glycol (4)  Ethene, iodoform and Ethylhydrogen sulphate OH

Q. 41. H 3C

CH3

+

H OH  → ? Product is :

(1)



(3)

CH3

(2) H3C

O

(4) O

CH3

O

H 3C

Q. 42. Cl2O is an anhydride of : (1) HClO4

(2) HOCl

(3) Cl2O3

(4) HClO2

Q. 43. In the reaction series –

KMnO4

SOCl

2 → P → CH3CHO  Q dil.H SO

2

4

CH COONa

3  → R. The product R is :

Heat

(1) (CH3CO) 2O (2) Cl. CH2COOCOCH3 (3) CH3COCH2COOH (4) Cl2. CHCOOCOCH3 Q. 44. In the reaction sequence : CH3CO X CH3CONH2 O CH3CO

Y Z  → CH3C ≡ N  → CH3COOC2H5

(1) NaOH, PCl5, Na + alcohol

(2) NH3, P2O5, aqueous ethanol/H+ (3) NH3, NaOH, Zn + NaOH (4) NH3, Conc. H2SO4, aqueous methanol Q. 45. Cyanides exists in : (1) Tautomeric form (2) Geometrical form (3) In both form (4) None Q. 46. Two hexoses were found to give the same osazone. Which one of the following statements is correct with respect to their structural relationship ? (1) The carbon atoms 1 and 2 in both have the same configuration (2) They are epimeric at C3 (3) The carbon atoms 3, 4 and 5 in both have the same configuration (4) Both must be aldoses

234

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 47. The simplest formula of a compound containing 50% of element X (at. wt. 10) and 50% of element Y (at. wt. 20) is : (1) XY (2) XY2 (3) X2Y (4) X2Y3 Q. 48. Which of the following is the most likely structure of CrCl3.6H2O, if 1/3 of total chlorine of the compound is precipitated by adding AgNO3 to its aqueous solution : (1) CrCl3.6H2O

Q. 55. Two gases A and B having molecular weights 60 and 45 respectively are enclosed in a vessel. The wt. of A is 0.50 g and that of B is 0.2 g. The total pressure of the mixture is 750 mm. Difference of partial pressure of the two gases is .......... mm.

(2) [Cr(H2O)3Cl3](H2O)3



(3) [CrCl2(H2O)4]Cl.2H2O (4) [CrCl.(H2O)5]Cl2.H2O Q. 49. Which of the following statements is not correct ? (1) All ores are minerals (2) All minerals are ores (3) All ores consists of gangue (4) Mineral consists of formula. Q. 50. Yellow ammonium sulphide solution is a suitable reagent used for the separation of : (1) HgS and PbS (2) PbS and Bi2S3 (3) Bi2S3 and CuS (4) CdS and As2S3

Section B Q. 51. A mixture of CuO and Cu2O contain 88% Cu. The percentage of CuO present in the mixture is .......... . Q. 52. The dye acriflavine, when dissolved in water, has its maximum light absorption at 4530 Å and its maximum fluorescence emission at 5080 Å. The number of fluorescene quanta is, on the average, 53% of the number of quanta absorbed. Using the wavelength of maximum absorption and emission, the percentage of absorbed energy emitted of fluorescence is .......... %. Q. 53. The amount (in gm) of sample containing 80% NaOH, required to prepare 60 litre of 0.5 M solution is .......... gm. Q. 54. If I.E. of F– is 328 kJ/mol and E.A. of F+ is 1681 kJ/mol, then E.N. of F at Pauling’s scale is .......... .

Q. 56. The Arrhenius equations for the rate constant of decomposition of methyl nitrite and ethyl nitrite are.



 –152300 Jmol –1  k1 (s-1) = 1013 exp   and   RT   –1  –157700 Jmol  -1 14 k2 (s ) = 10 exp     RT   respectively. The temperature at which the rate constants are equal is .......... k.

Q. 57. The conductivity of a saturated aqueous solution of Ag2C2O4 is 3.8 x 10–5 ohm–1 cm–1 at 25°C. The molar conductivity of oxalate ion is .......... Ohm–1cm2mol–1. Given at 25°C, conductivity of water is 6.2 x 10–6 ohm–1 cm–1 and molar conductivity of Ag+ at infinite dilution is 62 ohm–1cm2mol–1 and Ksp of Ag2C2O4 is 1.1 x 10–11 ? Q. 58. A crystal of lead(II) sulphide has NaCl structure. In this crystal the shortest distance between Pb+2 ion and S2– ion is 297 pm. The length of the edge of the unit cell in lead sulphide is .......... × 10–8 cm. Q. 59. A current of dry air was passed through a series of bulbs containing 1.25 g of a solute A2B in 50 g of water and then through pure water. The loss in weight of the former series of bulbs was 0.98 g and in the later series 0.01 g. If the molecular weight of A2B is 80. The degree of dissociation of A2B is ..........%. Q. 60. The pressure of the gas was found to decrease from 720 to 480 mm. When 5 g of sample of activated charcoal was kept in a flask of one litre capacity maintained at 27°C. If the density of charcoal at 1.25 gm/mL. The volume of gas adsorbed per gm of charcoal at 480 mm is .......... mL.

235

MOCK TEST PAPER-7

Mathematics 1 1 (1) (2) –   3 3 (3) 0 (4) 1 Q. 68. If ∆ABC is a scalene triangle, then the value of sin A sin B sin C cos A cos B cosC is ......... . 1 1 1

Section A Q. 61.

∫

4 + 5 sin x

dx equals : cos2 x (1) 4 tan x – sec x + c (2) 4 tan x + 5sec x + c (3) 9 tan x + c (4) 5 tan x – sec x + c 1

Q. 62.

∫ (x 0

dx 2

− 2 x + 2)3

=

3p + 8 32

p+1 4 2p (3) 0 (4) 3 Q. 63. The area between the parabola x2 = 4y and the line x – 4y + 2 = 0

(1)

(2)

(1) 9 8

(2) 9

9 9 (4) 2 4 Q. 64. The degree of the differential equation (3)

 d3 y   3   dx  (1) 1

2 /3

+4–3

d2 y dx 2

+5

dy = 0 is : dx

(2) 2

(3) 3 (4) 2/3 Q. 65. P ≡ (x1, y1, z1) and Q ≡ (x2, y2, z2) are two points. If direction cosines of a line AB are , m, n then projection of PQ on AB is : 1 1 1 (1) (x2 – x1) + (y2 – y1) + (z2 – z1) n  m (2)  (x2 – x1) + m (y2 – y1) + n (z2 – z1) 1 [(x2 – x1) + m(y2 – y1) + n(z2 – z1)] mn (4) mn [(x2 – x1) + m(y2 – y1) + n(z2 – z1)]

(3)

Q. 66. If ABCDE is a pentagon then the resultant of forces AB, AE, BC, DC, ED and AC in terms AB, AE, BC, DC, ED and of AC is : AB, AE, BC, DC, ED and AB,AC AE, BC, DC, ED(2) and3 AC (1) 2 AB, AE, BC, DC, ED and AB,AC AE, BC, DC, ED(4) 4 and AC (3) 5 Q. 67. The root of the equation 0 1 1   x     [x 1 2]  1 0 1   −1 = 0 is ..........  1 1 0   1 

(1) = 0 (2) ≠ 0 (3) can not say (4) depends on area Q. 69. From a pack of well shuffled cards, one card is drawn randomly. A gambler bets that it is either a diamond or a king. The odds in favour of his winning the bet will be : (1) 9 : 4 (2) 4 : 9 (3) 5 : 7 (4) 9 : 7 Q. 70. Let z1 = 10 + 6i, z2 = 4 + 6i and z is a complex  z − z1  p number such that amp   = , Then  z − z2  2 maximum value of z–7–9i is..... (1) 2 (3) 3

(2) 6 (4) 8

1 Q. 71. Find the values of x, if   2

(1) – 1 < x < –

2 5

2

(2) – 1 < x < – 0, (3) – 1 < x < –

,

5

2 5

,

2 5

4  log 2 log 1  x 2 −  5  5

BF3>BBr3 (4) BCl3>BBr3>BF3

H NH2

C=C

H H

(iii)

CH2Me

H CH3

C=C

CH3 (iv)

CH3 (1) i and ii

(2) i, ii and iii

(3) only ii

(4) in all of these

Q. 44. When 1-alkyne is treated with Na + LiQ. NH3 and product is reacted with methyl chloride, the end product of the reaction will be : (1)  Lower alkyne having two carbon less than 1-alkyne (2) Lower alkyne having one carbon less than 1-alkyne (3) Higher alkyne having one carbon more than 1-alkyne (4) Higher alkyne having two carbon more than 1-alkyne

254

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Cl 1 equivalent Mg

D O

2 → X  → Y is

Q. 45.

ether

Br Cl (1)



D (2)

D Br

D (3)



(4)

D

Br Cl D

Q. 46. In ‘nitration mixture’ concentrated sulphuric acid is used : (1) As sulphonating agent (2) As dehydrating agent (3) For the formation of nitronium ions (4) As a solvent Q. 47. Methanol and ethanol are distinguished by : (1) Treating with victor mayer test (2) Treating with Lucas reagent (3) Heating with iodine and alkali (4) Treating with CrO3 in dil. H2SO4 Q. 48. In which of the following crossed aldol condensations, only one kind of cross aldol is formed : (1) CH3CHO and CH3CH2CHO (2) CH3CHO and (CH3)2CO (3) (CH3)2CO and (C2H5)2CO (4) C6H5CHO and CH3CHO * COOH + NaHC O3

Q. 49.

COONa + CO2

C* is with in the product – (1) CO2

(2)

COONa

(3) Both (4) None of these Q. 50. Name the products in the acid- base reaction : (A) CH3CH2NH2 + HI (B) (CH3)3N + HBr (1) (A) Trimethyl ammonium iodide (B) Trimethyl ammonium bromide (2) (A) Ethyl ammonium iodide (B) Methyl ammonium bromide

(3) (A) Ethyl ammonium iodide (B) Trimethyl ammonium bromide (4) All of these

Section B Q. 51. Two substances A (t1/2 = 5 min) and (t1/2 = 15 min) are taken in such a way that initially [A] = 4[B]. The time after which both the concentration will be equal is .......... (assuming reactions are of first order). Q. 52. A radioactive element has atomic mass 90 amu and a half-life of 28 years. The number of disintegrations per second per g of the element is .......... × 1012. Q. 53. The standard free energy change for the reaction: H2(g) + 2AgCl(s)→ 2Ag(s) + 2H+(aq) + 2Cl–(aq) is –10.26 kcal mol-1at 25°C. A cell using above reaction is operated at 25°C under PH2 = 1 atm, [H+] and [Cl–] = 0.1. The e.m.f. of cell is .......... V. Q. 54. An element crystallizes into a structure which may be described by a cubic type of unit cell having one atom on each corner of the cube and two atoms on one of its body diagonals. If the volume of this unit cell is 24 × 10–24 cm3 and density of element is 7.2 g cm–3, the number of atoms present in 200 g of element is .......... × 1024 atoms. Q. 55. The concentration of an aqueous solution of common salt must be .......... g/l. If it is to be isotonic with a solution of this substance which freezes at –0.0186°C? (Assuming NaCl is fully ionized in the first solution). Q. 56. The coagulation of 10cm3 of Gold sol by 1 ml 10 % NaCl solution is completely prevented by addition of 0.025g of starch to it. The gold number of starch is .......... . Q. 57. NaBr, used to produce AgBr for use in photography can itself be prepared as follows : Fe + Br2→ FeBr2 FeBr2 + Br2→ Fe3Br8 (not balanced) Fe3Br8 + Na2CO3→ NaBr + CO2 + Fe3O4 (not balanced) To produce 2.50 × 10–3 kg NaBr, Fe will be consumed .......... × 10–3 kg.

255

MOCK TEST PAPER-9 Q. 58. The number of photons emitted in 10 hours by a 60 W sodium lamp is .......... × 1024 m. (lphoton = 5893 Å). Q. 59. At 500 kilobar pressure density of diamond and graphite are 3 g/cc and 2 g/cc respectively, at certain temperature ‘T’. The value of |∆H – DU| is .......... kJ/mol (kJ /mol) for the conversion of 1 mole of graphite to 1 mole of diamond at temperature ‘T’ .

Q. 60. 1 gm of an iron ore containing 50% ferrous (Fe2+) and ferric ion (Fe3+) and rest 50% impurities was dissolved in concentrated hydrochloric acid and the filtered solution was raised to 100 ml in flask. 50 ml of the solution were treated with M/10 K2Cr2O7, which give titre value of 5 ml. The percentage of ferric ion in the ore is .......... .

Mathematics 1 2 ( a1 + a22 + b12 + b22 ) 2 Q. 61. The number of x = [0, 2p] for which Q. 67. The equation of the tangent to the circle 2 sin 4 x + 18 cos2 x − 2 cos4 x + 18 sin 2 x = 1, is x2 + y2 + 4x – 4y + 4 = 0 which makes equal intercepts on the positive coordinate axis, is has number of solutions (1) x + y = 2 (2) x + y = 2 2 (1) 2 (2) 6 (3) x + y = 4 (4) x + y = 8 (3) 4 (4) 8 Q. 68. The other extremity of the focal chord of the 2 log b a log b x parabola y2 = 8x which is drawn at the point Q. 62. If a –5 x + 6 = 0 where a > 0, (1/2, 2) is : b > 0 and ab ≠ 1. Then the value of x is equal to (1) (2, –4) (2) (2, 4) log a log b (1) 2 b (2) 3 a (3) (8, –8) (4) (8, 8) log 2 log 3 (3) 2 a (4) a b Q. 69. The equations of tangents to the ellipse 9x2 + 16y2 = 144 which pass through the 1 1 1 1 1 1 Q. 63. Sum + + 2 + 2 + 3 + 3 +.... point (2, 3) are : 5 7 5 5 7 7 (1) x = 2 and y = – x + 5 5 3 (1) (2) (2) y = 3 and y = – x + 5 12 4 (3) y = 3 and x = 2 7 3 (3) (4) (4) x = 2 and y = 5 – x 12 49 Q. 70. The position of the point (2, 5) relative to the Q. 64. If x = 2 + 21/3 + 22/3, then the values of 3 2 hyperbola 9x2 – y2 = 1 is x – 6x + 6x is : (1) Inside (2) Outside (1) –2 (2) 3 (3) 4 (4) 2 (3) lie on (4) Cannot decide Q. 65. If the rth term is the middle term in the Q. 71 Let f : R → R be a function defined by 20 1   x 2 + 2x + 5 then the (r + 3)th expansion of  x 2 − f(x) = 2 is :  2x   x + x +1 (1) one-one and into term is : (in descending terms of x) (2) one-one and onto 1 1 (1) 20C14 ⋅ 14 . x (2) 20C12 ⋅ 12 . x 2 (3) many-one and onto 2 2 (4) many-one and into x 1 20 20 (3) – 13 · C7 · x (4) C13 ⋅ 13 cosθ + sinθ 2 2 Q. 72. lim = π π Q. 66. If the equation of the locus of a point θ→− θ + 4 equidistant from the point (a1, b1) and (a2, b2) is 4 (a1 – b2) x + (a1 – b2) y + c = 0, then the value (1) 2 (2) 1 of ‘c’ is (3) 2 (4) Does not exist 1 2 2 2 2 a12 + b12 − a22 − b22 (2) 2 a2 + b2 − a1 − b1 (1)

Section A

(

)

(3) a12 − a22 + b12 − b22

(4)

256

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

1  )  x +  [ x] when – 2 ≤ x ≤ 2, Q. 73. Let f ( x= 2  where [.] represents greatest integer function, then (1) f(x) is continuous at x = 2

(2) f(x) is continuous at x = 1 (3) f(x) is continuous at x = –1 (4) f(x) is discontinuous at x = 0 dy Q. 74. If x2ey + 2xyex = 0, then the value of dx when y = 0, x = 1 is :

−1 (1) 1+ e (3)

2 (2) 2+e

−2 1 + 2e

(4)

−1 2e + 1

Q. 75. If the tangent at P of the curve y2 = x3 intersect the curve again at Q and the straight lines OP, OQ make angles α, β with the x-axis tan α has the where ‘O’ is the origin then tan β value equal to : (1) –1

(2) –2

(3) 2

(4)

2

Q. 76. The length of largest continuous interval in which function f(x) = 4x – tan2x is monotonic, is π π (1) (2) 4 2 (3)

π 8

(4)

π 16

Q. 77. The set of value(s) of ‘a’ for which the ax 3 + ( a + 2)x 2 + ( a − 1) x + 2 3 possesses a negative point of inflection is : function f ( x )=

(1) (– ∞ , –2) ∪ (0, ∞) (2) {–4/5} (3) {–2, 0}

(4) empty set

Q. 78. The value of sin 10° sin 30° sin 50° sin 70° is :

(1)

1 16

(2)

1 32

1 18

(4)

1 36

(3)

Q. 79. If α is non real and α = 2|1+α+α

2

−2

−1

+α −α |

5

−1 then the value of

is equal to :

(1) 4

(2) 2

(3) 1

(4) 8

x −1 y − 2 z −3 = = and −3 2k 2 x −1 y − 5 z −6 = = are at right angles, then 3k 1 −5 the value of k will be : 10 7 (1) − (2) − 10 7 Q. 80. If

the

lines

(3) –10

(4) –7

Section B Q. 81. For ∆ABC, let position vectors of A, B and C be respectively 6ˆi + ˆj + kˆ, 2ˆi + 4 ˆj + kˆ and 4ˆi + 4 ˆj + 7 kˆ . If interior and exterior bisectors of angle A meets BC at D and E respectively 1 1 1 − = , then [k] is equal to .......... and BD BE k Q. 82. The area of the region enclosed between the = y | x | 4 − x 2 is 2k, curves y + 4 = x2 and then the value of k is .......... .

Q. 83. Let lim n8 n →∞

n



∑  r r =1

r7 16

16

+n

equal to .......... .

 π , then k is  =  4k

∞

Q. 84. The value of

∫ [x].2

−[ x ]

dx is equal to ..........

0

(where [.] denotes greatest integer function) Q. 85. Let A be the set of all 3 × 3 symmetric matrices whose diagonal elements are 1, then the number of matrices A for which  x  1      the system of linear equations A  y  = 0   z  0  represents three perpendicular planes is .......... . 1 cos α − sin α cos α + sin α 1 cos α sin α cos β = + sin β k 1 cos β sin β , 1 cos γ − sin γ cos γ + sin γ 1 cos γ sin γ

Q. 86. If 1 cos β − sin β

then the value of ‘k’ is .......... . Q. 87. The curve y = ƒ(x) passes through the 3

dy + ydx = 11 . Let a origin and satisfies dx

∫ 0

and b are chosen randomly from the set S = {1, 2, 3,........ 10} with replacement. If the probability that the curve y = ƒ(x) passes p (where p and q are through (a, b) is q coprime), then (p + q) is .......... .

257

MOCK TEST PAPER-9 π Q. 88. sin (A + 2B) = cos (2A + B) and B – A = 3 B  π π where A, B ∈  − ,   , then is .......... . A  2 2 Q. 89. If the set of values of x satisfying the inequality tan x . tan 3x < –1 in the interval

π   36( b − a )   0,  is (a, b), then the value of   2 π    is .......... . Q. 90. If sin2x cosy = (a2 – 1)2 + 1 and cos2x sin  y = a + 1, where x, y ∈ [0, p] and a ∈ R, then number of ordered pairs (x, y) is .......... .

Answers Physics Q. No.

Answer

Topic Name

Q. No.

Answer

Topic Name

1

(1)

Calorimetry

16

(1)

Law of Motion

2

(3)

Kinetic Theory of Gases

17

(2)

Current Electricity

3

(1)

Heat Transfer

18

(4)

Alternating Current

4

(1)

Sound Wave

19

(2)

Electrostatics

5

(1)

Reflection at Plane Surface

20

(1)

Fluid Mech

6

(1)

Refraction at Plane Surface

21

16

7

(2)

Prism

22

205.00

8

(1)

Interference

23

2.00

Conservation Law

9

(3)

Wave Nature of Light Diffraction

24

48.00

Rotational Motion

Work Energy and Power Physical Thermodynamics

10

(3)

Solid and Semi-conductor

25

1.20

Electrostatics

11

(1)

Photo Electric Effect

26

4.00

Capacitance

12

(3)

Matter Wave

27

2.00

Current Electricity

13

(2)

X-Ray

28

9.00

Basic Math

14

(3)

Nuclear Fission

29

4.00

Ray Optics

15

(1)

Unit and Dimension

30

5.00

Elasticity

Chemistry Q. No.

Answer

Q. No.

Answer

31

(1)

Periodic Table

Topic Name

46

(3)

Topic Name Aromatic Compound

32

(4)

Chemical Bonding

47

(3)

Alcohol, Ether and Phenol

33

(2)

Gaseous State

48

(4)

Carbonyl Compound

34

(3)

Chemical Energetic

49

(1)

Carboxylic Acid

35

(2)

Chemical Equilibrium

50

(3)

Nitrogen Compound

36

(3)

Ionic Equilibrium

51

15.00

Chemical Kinetics

37

(1)

IUPAC

52

5.24

Nuclear Chemistry

38

(1)

Isomerism

53

0.34

Electrochemistry

39

(4)

Hydrogen and Its Compounds

54

3.472

Solid State

40

(2)

p-Block-Boron

55

0.2925

Solution

41

(3)

p-Block-Carbon

56

25.00

Surface Chemistry

42

(1)

s-Block Elements

57

5.376

Mole Concept

43

(2)

General Organic Chemistry

58

6.40

Atomic Structure

44

(3)

Hydrocarbon

59

100

Thermodynamics

45

(1)

Halogen Dervitative

60

16.40

Hydrogen and Its Compounds

258

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Mathematics Q. No.

Answer

61

(4)

62

Topic Name

Q. No.

Answer

Topic Name

Trigonometry

76

(2)

Monotonicity

(2)

Logarithms

77

(1)

Maxima and Minima

63

(1)

Progressions

78

(1)

Properties of Triangle

64

(4)

Theory of Equation

79

(1)

Complex Numbers

65

(3)

Binomial Theorem

80

(1)

Three Dimensional Plane

66

(2)

Straight Line & Point

81

10.00

Vectors

67

(2)

Circles

82

16.00

Area Under Curve

68

(3)

Parabola

83

8.00

Indefinite Integration

69

(2)

Ellipse

84

2.00

Definite Integration

70

(1)

Hyperbola

85

5.00

Metrics

71

(4)

Functions

86

2.00

Determinants

72

(1)

Limits

87

21.00

Probability

73

(4)

Continuity

88

3.00

Trigonometic Ratios

74

(3)

Differentiation

89

3.00

Trigonometric Equations

75

(2)

Tangent and Normal

90

1.00

Trigonometric Equations



MOCK TEST PAPER 10 Time : 3 Hours

Total Marks : 300

General Instructions : 1. 2. 3. 4. 5. 6.

There are three subjects in the question paper consisting of Physics (Q. no. 1 to 30), Chemistry (Q. no. 31 to 60) and Mathematics (Q. no. 61 to 90). Each subject is divided into two sections. Section A consists of 20 multiple choice questions & Section B consists of 10 numerical value type questions. In Section B, candidates have to attempt any five questions out of 10. There will be only one correct choice in the given four choices in Section A. For each question 4 marks will be awarded for correct choice, 1 mark will be deducted for incorrect choice for Section A questions and zero mark will be awarded for not attempted question. For Section B questions, 4 marks will be awarded for correct answer and zero for unattempted and incorrect answer. Any textual, printed or written material, mobile phones, calculator etc. is not allowed for the students appearing for the test. All calculations / written work should be done in the rough sheet is provided with Question Paper.

Physics (1)

Section A Q. 1. If energy E, velocity (V) and time (T) are chosen as the fundamental quantities, then the dimensions of surface tension will be : (1) [EV –2T –1] (2) [EV –1T –2] (3) [EV –2T –2] (4) [E –2V –1T –3]  Q. 2. A vector P1 is along the positive x-axis.  If P its vector product with another vector 2 is  zero, then P2 could be : (1) 4 ˆj (2) −4iˆ ( ˆj + kˆ) (3) (4) −(ˆi + ˆj ) Q. 3. The trajectory of a projectile in a vertical plane is y = ax – bx2, where a and b are constants and x and y are respectively horizontal and vertical distances of the projectile from the point of projection. The maximum height attained by the particle and the angle of projection from the horizontal are: (1)

b2 , tan −1 ( b ) 2a

(2)

a2 , tan −1 (2 a ) b

a2 2a2 , tan −1 ( a ) , tan −1 ( a ) (3) (4) 4b b Q. 4. A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block is :

Pm M+m

(2)

Pm M–m

PM M+m Q. 5. A block of mass m slides down an inclined right angled trough as shown in the figure. If the coefficients of kinetic friction between block and material composing the trough is mk, find the acceleration of the block : (3) P

(4)

Trough



(1) g(sin q – 2 µ k cos q) (2) g(sin q –mk cos q) (3) g(sin q –2mk cos q) (4) g(sin q – µ k cos q) Q. 6. An insulating solid sphere of radius ‘R’ is charged in a non-uniform manner such that A volume charge density r = , where A is a r positive constant and r is the distance from centre. Electric field strength at any inside point at distance r1 is : 1 4 πA 1 A (1) (2) 4 πε0 r1 4 πε0 r1 A A (3) (4) πε0 2ε0

260

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 7. Two metallic charged spheres whose radii are 20 cm and 10 cm, respectively, each having 150 mC positive charge. The common potential after they are connected by a conducting wire is : (1) 9 × 106 V (2) 4.5 × 106 V (3) 1.8 × 107 V (4) 13.6 × 106 V Q. 8. In an experiment according to set up, E1 = 12 volt having zero internal resistance and E = 2 volt. The galvanometer reads zero, then X (in ohm) would be : 500 Ω

A

B

G

E1

XΩ

E C

D

(1) 200 (2) 500 (3) 100 (4) 10 Q. 9. A current I flowing through the loop as shown in the adjoining figure. The magnetic field at centre O is :

(1)

7m0 I Ä 16 R

(2)

× ×

3 × C ×

1

× 2

3 2 H (3) H (4) p p Q. 13. Consider a solid cube of uniform charge density of insulating material. What is the ratio of the electrostatic potential at a corner to that at the centre: (Take the potential to be zero at infinity, as usual) 1 1 (2) (1) 2 1 1 1 (3) (4) 4 9 Q. 14. A solid of mass 2 kg is heated and ∆H (Heat given) vs Dq (change in temperature) is plotted. Specific heat of solid is :

7m0 I • O 16 R

5m0 I 5m0 I Ä (4) (3) O· 16 R 16 R Q. 10. A uniform but time varying magnetic field exists in cylindrical region and directed into the paper. If field decrease with time and a positive charge placed at any point inside the region. Then it moves : ×

p p volt (2) volt 10 20 (3) 20 p milli volt (4) 100 p milli volt Q. 12. A bulb is rated at 100 V, 100 W, it can be treated as a resistor. Find out the inductance of an inductor (called choke coil) that should be connected in series with the bulb to operate the bulb at its rated power with the help of an ac source of 200 V and 50 Hz. p H (2) 100 H (1) 3

(1)

P× 4 ×

(1) along 1 (2) along 2 (3) along 3 (4) along 4 Q. 11. A copper disc of radius 0.1 m is rotated about its centre with 20 revolution per second in a uniform magnetic field of 0.1 T with its plane perpendicular to the field. The emf induced across the radius of the disc is :

H (in kJ) 45° (in °C)

(1) 1 J/kg/°C (2) 0.5 J/kg/°C (3) 2 kJ/kg/°C (4) 0.5 kJ/kg/°C Q. 15. A parallel plate capacitor of plate area A and separation d is provided with thin insulating spacers to keep its plates aligned in an environment of fluctuating temperature. If the coefficient of thermal expansion of material of plate is a then the coefficient of thermal expansion (aS) of the spacers in order that the capacitance does not vary with temperature (ignore effect of spacers on capacitance) a (1) aS = (2) aS = 3a 2 (4) aS = a (3) aS = 2a

261

MOCK TEST PAPER-10 Q. 16. A wire is 4 m long and has a mass 0.2 kg. The wire is kept horizontally. A transverse pulse is generated by plucking one end of the taut (tight) wire. The pulse makes four trips back and forth along the cord in 0.8 sec. The tension is the cord will be : (Assume uniform tension throughout the wire) (1) 80 N (2) 160 N (3) 240 N (4) 320 N Q. 17. Consider a plane standing sound wave of frequency 103 Hz in air at 300 K. Suppose the amplitude of pressure variation associated with this wave is 1 dyne/cm2. The equilibrium pressure is 106 dyne/cm2. The amplitude of displacement of air molecules associated with this wave is : (Given speed of sound : 340 m/s Molar mass of air : 29 × 10–3 kg/mol) (1) 4 × 10–6 m (2) 40 × 10–6 m (3) 400 × 10–6 m (4) 40000 × 10–6 m Q. 18. In RLC circuit, at a frequency v, the potential different across each device are (DVR)max = 8.8 V, (DVL)max = 2.6 V and (DVC)max = 7.4 V. The combined potential difference (DVL + DVC)max across the inductor and capacitor is : (1) 10 V (2) 7.8 V (3) 7.4 V (4) 4.8 V Q. 19. A body is heated to temperature 40° and kept in a chamber maintained at 20°. If temperature decreases to 36° in 2 minutes. Time after it will further decrease by 4° is : (1) 2 min (2) 2 min 33 sec (3) 2 min 55 sec (4) 3 min Q. 20. A gas is taken through a cyclic process ABCA as shown in figure. If 3.6 calories of heat is given in the process, one calorie is equivalent to : V(cm)3

850

650

C

A

250

(1) 4.20 J (3) 4.18 J

B

400

(2) 4.19 J (4) 4.17 J

(kPa)

Section B Q. 21. A block of mass m = 1 kg moving on horizontal surface with speed u = 2 m/s enters a rough horizontal patch ranging from x = 0.10 m to x = 2.00 m. If the retarding force fr on the block in this range is inversely proportional to x over this range i.e. −k fr = , 0.10 < x < 2.00 x = 0 for x < 0.10 and x > 2.00 If k = 0.5 J then the speed of this block as it crosses the patch is .......... m/s. (use ln 20 = 3) Q. 22. A sphere of mass m = 0.5 kg carrying positive charge q = 110 mC is connected with a light, flexible and inextensible spring of length r = 60 cm and whirled in a vertical circle. If a vertically upwards electric field of strength E = 105 N/C exists in the space then the minimum velocity of sphere .......... m/s required at highest point so that it may just complete the circle is (g = 10 m/s2) Q. 23. The electric potential difference between two points is 50kV. If a charge of 20C, having a mass of 200 kg, is placed at the high-potential end, then find the final speed of the charge as it reaches the low- potential end in m s–1 is....... Q. 24. A uniform ball of radius R = 10 cm rolls without slipping between two rails such that the horizontal distance is d = 16 cm between two contact points of the rail to the ball. If the angular velocity is 5 rad/s, then the velocity of centre of mass of the ball is .......... cm/s. Q. 25. A smooth vertical conducting tube have two different section is open from both ends and equipped with two piston of different areas. Each piston slides in respective tube section. 1 liter of ideal gas at pressure 1.5 × 105 Pa is enclosed between the piston connected with a light rod. The cross section area of upper piston is 10p cm2 greater than lower one. Combined mass of two piston is 1.5 kg. If the piston is displaced slightly. Time period of oscillation will be .......... × 10–1 s.

262

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 26. In determination of young modulus of elasticity of wire, a force is applied and extension is recorded. Initial length of wire is ‘1 m’. The curve between extension and stress is depicted then young modulus of wire will be K × 109 N/m2, where K is .......... × 109 N/m2.

Q. 28. A thin isosceles prism with angle 4° and refractive index 1.5 is placed inside a transparent tube with water (refractive 5 index = ) as shown. The deviation of light 4 whether upward or downward due to prism will be in degree is ...........

4 mm Ext. 2 mm 4000

8000 Stress

Q. 27. A very expensive diamond is polished into a perfect sphere of radius 5 cm. The back surface of the sphere is then covered with silver. If d is the distance of source of light from surface of sphere so that image coincide with the source. The index of refraction of diamond is 2.4, then d = .......... cm.

S

d

Q. 29. Consider the interference at P between waves emanating from three coherent sources in same phase located at S1, S2 and S3. If intensity due to each source is d2 λ I0 = 12 W/m2 at P and = then 2D 3 resultant intensity at P will be .......... W/m2. Q. 30. When the voltage applied to an X-ray tube is increased from 10 kV to 20 kV, the wavelength interval between the ka line the short wave cut off the continuous X-Ray spectrum increases by a factor of 3. The atomic number of element for which the tube anticathode is made, is ........... (Rydberg’s constant 107 m–1).

Chemistry Section A Q. 31. Polarisation may be called as the distortion of the shape of an anion by an adjacently placed cation. Which of the following statements is/are correct ? (1) Lesser polarization is brought about by a cation of low radius (2)  A large cation is likely to bring about a large degree of polarization (3)  Larger polarisation is brought about by a cation of high charge (4)  A small anion is likely to undergo a large degree of polarisation Q. 32. Lanthanide contraction is related with : (1)  Sharp decrease in atomic size in lanthanide series



(2)  Slow or gradual decrease in atomic size in lanthanide series

(3) Constancy in atomic size (4) All of the above Q. 33. The compound which has one isopropyl group is : (1) 2, 2, 3, 3-tetramethyl pentane (2) 2, 2-dimethyl pentane (3) 2, 2, 3-trimethyl pentane (4) 2-methyl pentane Q. 34. CH3–CH2–CH2–CH3. There is free rotation about (C2 s C3) bond. The same most stable form is repeated after rotation of : (1) 60°

(2) 120°

(3) 240°

(4) 360°

263

MOCK TEST PAPER-10 Q. 35. The reaction H2S + H2O2 → S + 2H2O manifests : (1) Acidic nature of H2O2 (2) Alkaline nature of H2O2 (3) Oxidising action of H2O2 (4) Reducing nature of H2O2 Q. 36. Alumina is insoluble in water because ........ . (1) It is a covalent compound (2)  It has high lattice energy and low heat of hydration (3)  It has low lattice energy and high heat of hydration (4)  Al3+ and O2– ions are not excessively hydrated. Q. 37. The soldiers of Napolean army while at Alps during freezing winter suffered a serious problem as regards to the tin buttons of their uniforms. White metallic tin buttons get converted to grey powder. This transformation is related to (1)  An interaction with water vapour contained in humid air (2) A change in crystalline structure of tin (3)  A change in the partial pressure of O2 in air (4)  An interaction with N2 of air at low temperature Q. 38. The metal X is prepared by the electrolysis of fused chloride. It reacts with hydrogen to form colourless solid from which hydrogen is released on treatment with water. The metal is : (1) Al (2) Ca (3) Cu (4) Zn Q. 39. HCHO with conc. alkali forms two compounds. The change in oxidation number would be : (1) (0 to –2) in both the compounds (2) (0 to +2) in both the compounds (3)  (0 to +2) in one compound and (0 to –2) in the second compound (4) All are correct Q. 40. OHC–CH2–CH2 –CH2–CH2–OH O



is converted into

O by :

(1) (i) KMnO4 (ii) H+, ∆H (2) (i) Na2Cr2O7 (ii) H+, ∆ (3) (i) Ag2O (ii) H+, ∆ (4) All of these NH–CO–CH3 HNO3/H2SO4

Q. 41.

X

H2O/H+ heat

Z, Z is :

NH2

NH2 (1)

(2)

NO2

NO2 NH2

NHCOCH3 (3)

NO2

(4)

NO2

O2 N NO2

Q. 42. Glycoside linkage is : (1) an amide linkage (2) an ether linkage (3) an ester linkage (4) none of these Q. 43. Dumas method involves the determination of nitrogen content in the organic compound in form of (1) NH3 (2) N2 (3) NaCN (4) (NH4)2SO4 Q. 44. In which of the following molecules, the substituent does not exert its resonance effect? ⊕ (1) C6H5NH2 (2) C6 H5 N H3 (3) C6H5OH (4) C6H5Cl Q. 45. The reduction of oct-4-yne with H2 in the presence of Pd/CaCO3 – quinoline gives (as a major product) –(Hydrocarbon) (1) trans-oct-4-ene (2) cis-oct-4-ene (3) a mixture of cis and trans-oct-4-ene (4) a completely reduced product C8H18 Q. 46. The species responsible for nitration and sulphonation by nitric acid conc. H2SO4 and fuming H2SO4 are : (1) NO2 and SO3 ⊕

N O2 and SO3 (2) ⊕

N O and SO2 (3) (4) NO2 and SO2

264

Oswaal JEE (Main) Mock Test 15 Sample Question Papers H O+

3 ® C4H10O Q. 47. Ester A (C4H8O2)+ CH3MgBr¾¾¾ (2 parts) (alcohol) (B) Alcohol B reacts slowly with sodium metal. Hence A and B are O || (1) CH3–C–O–C2H5, (CH3)3COH

O || (2) H–C–O–C3H7 , (CH3)2CHOH O || (3) CH3–C–O–C2H5, (CH3)2CHOH

Q. 52. 28.0 g of N2 gas at 350 K and 25 atm was allowed to expand isothermally against a constant external pressure of 1 atm. The value of ‘q’ for the gas is .......... J. Q. 53. In the preparation of quick lime from lime stone, the reaction is: CaCO3(s)  CaO(s) + CO2(g)



O || H–C–O–C3H7, (CH3)3COH (4)

Q. 48. Oxalic acid + A →

O

O O

Q. 54. Two particles A and B are in motion. If the wavelength associated with the particle A –8 is 5 × 10 m, if its momentum is half of A. Then the wavelength of particle B is .......... –8 × 10 m.

O

conc. H 2 SO4

hence A ¾¾¾¾¾® B, B is :

(1)

H 2C

O

H2C

O

CH2

(2)

CH2

CH2 – O – CH2 (3)

O

O O

(4) None of these

OH

OH

Experiments carried out between 850°C and 950°C led to set of Kp values fitting an empirical equation 8500 log Kp = 7.282 – T where T is absolute temp. If the reaction is carried out in quite air, the temperature predicted from this equation for complete decomposition of the lime stone would be .......... K.

–7

Q. 49. pH of 10 M HCl solution is : (1) 7 – log2 (2) 7 – log 1.618 (3) 7 (4) 6.95 Q. 50. A gas at a pressure of 5.0 atm is heated from 0° to 546 °C and simultaneously compressed to one-third of its original volume. Hence final pressure is : (1) 10.0 atm (2) 30.0 atm (3) 45.0 atm (4) 5.0 atm

Section B Q. 51. In an ore the only oxidizable material is Sn2+. This ore is titrated with a dichromate solution containing 2.5 g of K2Cr2O7 in 0.50 litre. A 0.40 g sample of the ore required 3 10.0 cm of titrant to reach equivalence point. The percentage of tin in ore is .......... . (K = 39.1, Cr = 52, Sn = 118.7)

Q. 55. At room temperature (20°C) orange juice gets spoilt in about 64 hours. In a refrigerator at 3°C juice can be stored three times as long before it gets spoling. The time taken by juice to get spoilt at 40°C is .......... hours. Q. 56. The voltage of the cell :

Pb|PbSO4| Na2SO4.10H2O (salt)|Hg2SO4| Hg



is + 0.9647 at 25°C. The temperature –4 –1 coefficient is 1.74 × 10 V. K .



–1 –1 The values of DS is .......... ak mol .

Q. 57. An element crystallizes in a structure having FCC unit cell of an edge 200 pm. The density, 23 if 200 g of this element contains 24 × 10 3 atoms is .......... g cm . Q. 58. 1.5 g of a monobasic acid when dissolved in 150 g of water lowers the freezing point by 0.165°C. 0.5 g of the same acid when titrated, after dissolution in water, requires 37.5 ml of N/10 alkali. The degree of dissociation of the acid is .......... %. (Kf for –1 water = 1.86°C mol ). Q. 59. In order to coagulate 400 ml of Fe(OH)3 sol completely 60 ml of 0.1M KCl is required. The coagulation power of KCl will be .......... .

265

MOCK TEST PAPER-10 Q. 60. The standard molar enthalpies of formation of IF3 (g) and IF5 (g) are –470 kJ and –847 kJ, respectively. Valence shell electron pair repulsion theory predicts that IF5 (g) is square pyramidal in shape in which all I–F bonds are equivalent while IF3 (g) is T-shaped (based on trigonalbipyramidal geometry) in which I–F bonds are of



different lengths. It is observed that the axial I–F bonds in IF3 are equivalent to the I–F bonds in IF5. The equatorial I–F bond strength in IF3 is .......... kJ/mol. Some other informations given are : I2 (s) → I2 (g) ; ∆H = 62 kJ F2 (g) → 2F (g); ∆H = 155 kJ I2 (g) → 2 I (g) ; ∆H = 149 kJ

Mathematics Section A Q. 61. (1) Let z ∈ C be such that |z|< 1. If 53z ,then:  5 1  z 

Q. 66. The coefficient of xm in

(1 + x)k + (1 + x)k + 1 + ….. + (1 + x)n, (k ≤ m ≤ n), is given by

(1) 5 Re (ω) > 4

(2) 4 Im (ω) > 5

(1) n+1Cm

(2) nCm

(3) 5 Re (ω) > 1

(4) 5 Im (ω) < 1

n–1 (3) Cm – 1

(4)

(4) ~ q 2

Q. 63. The inequality log4 (2x + x + 1) 7π – log2 (2x – 1) ≤ – tan satisfies for all 4 (1) x ≥ – 1

(2) x ≥ 1

(3) x ≤ – 1

(4) x ≥ 0

(1) rational

(2) irrational

(3) real

(4) imaginary

Q. 65. If a, b, c be the first, third and nth terms respectively of an A.P., then sum to n terms is : (1)

2

2

c+a c −a c+a c −a + (2) – 2 2 b−a b−a 2

2

2

2

c +a c+a c +a c+a (3) + (4) + b−a b+a 2 2

(1) 560

(2) 590

(3) 90

(4) 360

Q. 68. The area of the pentagon whose vertices are (4, 1), (3, 6), (–5, 1), (–3, –3) and (–3, 0) is :

Q. 64. If the roots of the equation ax2 + x + b = 0 be real and different, then the roots of the equation x2 – 4 ab x + 1 = 0 will be :

2

Cm + 1

Q. 67. How many numbers of four digits greater than 2300 can be formed with the digits 0, 1, 2, 3, 4, 5 and 6; no digit being repeated in any number ?

Q. 62. (3) The logical statement (p ⇒ q) ∧ (q ⇒ ~ p) is equivalent to: (1) p (2) q (3) ~ p

n+1

(1) 30 unit2

(2) 60 unit2



(4) 150 unit2

(3) 120 unit2

Q. 69. The equation to the circle which passes through the points (1, –2) and (4, –3) and which has its centre on the straight line 3x + 4y = 7 is : (1) 15x2 + 15y2 + 94x + 18 y + 55 = 0 (2) 15x2 + 15y2 – 94x – 18 y + 55 = 0 (3) 15x2 + 15y2 – 94x + 18 y + 55 = 0 (4) 15x2 + 15y2 + 94x – 18 y – 55 = 0

2

Q. 70. The vertex, focus, directrix and length of the latus rectum of the parabola y2 – 4y – 2x – 8 = 0 are respectively equals to

266

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

 11  (1) A(6, 2), S  − , 2   2  Eq. of directrix x = –    11  (2) A(–6, 2), S  , 2   2 

Eq. of directrix x = –  

 11  (3) A(–6, 2), S  − , 2   2 

Eq. of directrix x = –  

 11  (4) A(–6, 2), S  − , 2   2 

13 , L. of L.R. = 2 2

13 , L. of L.R. = 3 2 13 , L. of L.R. = 2 2

13 and L.L.R. = 2 2 y x Q. 71. The equation cos q – sin q = 1 will a b y2 x2 touch ellipse 2 + 2 = 1 at point P a b whose eccentric angle is : (1) q (2) (p – q) (3) (p + q) (4) 2p – q Q. 72. The equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13 is : (1) 9x2 – 144 y2 = 900 (2) 25x2 – 144 y2 = 900 (3) 25x2 – 144 y2 = 200 (4) 25x2 – 36y2 = 900 Q. 73. Which of the following function from A = {x : –1 ≤ x ≤ 1} to itself is bijection : x  πx  (1) f(x) = (2) g(x) = sin   2  2  2 (3) h(x) = |x| (4) k(x) = x Q. 74. Let f(a) = g(a) = k and their nth derivatives exist and are not equal for some n. Further if lim f ( a ) g ( x ) − f ( a ) − g ( a ) f ( x ) + g ( a ) = 4 x →a g( x ) − f ( x )

Eq. of directrix x =

then k is equal to : (1) 0 (3) 2  1 if x is Q. 75. If f(x) =  −1 if x is

(2) 4 (4) 1 rational is continuous irrational

(1) ∨ x ∈ R (2) for no real values of x ∨ x ∈ ( −1, 1 ) (3) (4) ∨x∈R (–1, 0, 1)

Q. 76. Differentiation of loge x w. r. t. log1/5 x is : 1 1 (1) log e (2) – log e 5 5 (3) log1/5 e (4) log 5e Q. 77. All the points on the curve y = x + sin x at which the tangents are parallel to x axis lie on (1) straight line (2) circle (3) parabola (4) ellipse Q. 78. In a submarine telegraph cable the speed 1 of signaling varies as x2 log   where x is x the ratio of the radius of the cable to that of covering. Then the greatest speed is attained when this ratio is : (1) 1 : e (2) e : 1 (3) e : 1 (4) 1 : e Q. 79. Let the complex numbers z1, z2, z3 represent vertices of an equilateral triangle. If z0 be the circumcentre of the triangle then z12 + z22 + z32 = (1) z02 (2) 2z02 (3) 3z02 (4) 9z02 Q. 80. The projections of a line segment on x, y and z axes are respectively 3, 4 and 5, then the length and direction cosines of the line segment are respectively equal to : (1) 5

2;

(2) 3 2; (3) 5 2; (4) 3 2;

3

,

5 2 3

,

3 2 3 5 2 3 5 2

, ,

4

,

5 2 4

,

5 2 4 3 2 4 5 2

1 2 1 2 1

,

2

,–

1 2

Section B Q. 81. If the value of expression sin 5°. si n55°sin 115° can be expressed as

a −b

, then

c + 4b is 11a

c equal to .......... (where a, b, c are mutually

coprime) Q. 82. If the solution set of inequality  3  1  cos x +   cos x −  ≤ 0 in [0, 2p] is , 2 2   

267

MOCK TEST PAPER-10  απ βπ   γπ δπ  +  6 , 6  ∪  6 , 6  where a, b, g, d ∈ I ,     then the value of |b − a + d − g| is .......... .

Q. 83. If x and y are positive integers satisfying, 1 1 1 tan −1   + tan −1   = tan −1   then the x y   7   number of ordered pairs of (x, y) is : Q. 84. In a tournament, four players are participating. Each player plays with every other player. Each player has 50% chance of winning any game and there are no ties. If the probability that at the end of tournament there is neither a winless nor a an undefeated player is there is , where b a and b are relatively prime integers then |2a – b| is equal to .......... . 1 3 cos θ 1 1 3 cos θ , then value of Q. 85. If ∆ = sin θ 1 sin θ 1 ∆ max is ........... 2

4 6 2 3  Q. 86. Let A =  ,B =   and C = A +  −9 −6  3 4  A2B + A3B2+...... A100B99. If sum of elements of matrix CB is l then 36 + l is .......... . 2 cos x

is f(x) + sin x − cos x π and φ(0) = n( e 2 − e ) , then φ   is equal 4 to .......... .

Q. 87. If primitive of

e

x +1

0

Q. 88.

∫ (| x + 1| +[x + 3]) dx (where

[.]

denotes

−4

greatest integer function) is equal to Q. 89. The shortest distance between the curve y = x4 + 3x2 + 2x and the straight line 1 y = 2x – 1 is expressed as , then p is p Q. 90. Curve satisfying differential equation x(y2 + x)dx + x2ydy = 0 passes through 3 3 , 0 , then value of  y 2 ( −2 )  is ........... , where [.] denotes greatest integer function.

(

)

Answers Physics Q. No.

Answer

1

(3)

2

(2)

3

Topic Name

Q. No.

Answer

Topic Name

Unit & Dimension

16

(1)

Transverse Wave

Vector

17

(3)

Sound Wave

(3)

Projectile

18

(4)

Doppler Effect

4

(4)

Newton’s Law of Motion

19

(2)

Radiation

5

(1)

Friction

20

(4)

Kinetic Theory of Gases

6

(4)

Electrostatics

21

1.00

Work, Power and Energy

7

(1)

Capacitance

22

6.00

Circular Motion

8

(3)

Current Electricity

23

100.00

Conservation Law

9

(1)

Magnetic Effect of Current

24

30.00

Rotational Motion

10

(3)

Magnetism

25

5.0

Simple Harmonic Motion

11

(3)

Electromagnetic Induction

26

2.00

Elasticity

12

(4)

Alternating Current

27

25.00

Reflection at Curve Surface

13

(2)

Gauss’s Law

28

0.80

Prism

14

(4)

Heat Transfer

29

36.00

Wave Optics

15

(3)

Thermal Expansion

30

30.00

X-Ray

268

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Chemistry Q. No.

Answer

Q. No.

Answer

31

(3)

Topic Name Chemical Bonding

46

(2)

Topic Name Aromatic Compound

32

(2)

Periodic Table

47

(1)

Halogen Derivatives

33

(4)

IUPAC

48

(1)

Alcohol, Ether, Phenol

34

(4)

Isomerism

49

(1)

Ionic Equilibrium

35

(3)

Hydrogen Family

50

(3)

Gaseous State

36

(1)

p-Block –Boron Family

51

15.13

Redox Reaction

37

(2)

p-Block- Carbon Family

52

2795

Chemical Energetics

38

(2)

s-Block

53

1667.26

39

(3)

Carbonyl Compound

54

10.00

Atomic Structure

40

(3)

Carboxylic Acid

55

6.40

Chemical Kinetics

41

(2)

Nitrogen Containing

56

8.02

Electrochemistry

42

(2)

Biomolecules

57

41.60

Solid State

43

(2)

Practical Chemistry

58

18.28

Solution

44

(2)

General Organic Chemistry

59

2.00

Surface Chemistry

45

(2)

Hydrocarbon

60

272

Thermochemistry

Chemical Equilibrium

Mathematics Q. No.

Answer

61

(3)

Topic Name Complex number

Q. No.

Answer

76

(1)

Topic Name Differentiation

62

(3)

Mathematical Reasoning

77

(3)

Tangent and Normal

63

(2)

Inequalities

78

(1)

Maxima and Minima

64

(4)

Quadratic Equation

79

(3)

Complex Number

65

(1)

Progression

80

(1)

Three Dimensional Plane

66

(4)

Binomial Theorem

81

4.00

Trigonometry Ratio

67

(1)

Permutation and Combination

82

6.00

Trigonometric Equation

68

(1)

Straight Line

83

6.00

Inverse Trigonometric Functions

69

(3)

Circle

84

2.00

Probability

70

(3)

Parabola

85

10.00

Determinant

71

(4)

Ellipse

86

7.00

Matrices

72

(2)

Hyperbola

87

2.00

Indefinite Integration

73

(2)

Function

88

7.00

Area Under Curve

74

(2)

Limit

89

5.00

Mamima and Minima

75

(2)

Continuity

90

1.00

Differential Equation



MOCK TEST PAPER 11 Time : 3 Hours

Total Marks : 300

General Instructions : 1. 2. 3. 4. 5. 6.

There are three subjects in the question paper consisting of Physics (Q. no. 1 to 30), Chemistry (Q. no. 31 to 60) and Mathematics (Q. no. 61 to 90). Each subject is divided into two sections. Section A consists of 20 multiple choice questions & Section B consists of 10 numerical value type questions. In Section B, candidates have to attempt any five questions out of 10. There will be only one correct choice in the given four choices in Section A. For each question 4 marks will be awarded for correct choice, 1 mark will be deducted for incorrect choice for Section A questions and zero mark will be awarded for not attempted question. For Section B questions, 4 marks will be awarded for correct answer and zero for unattempted and incorrect answer. Any textual, printed or written material, mobile phones, calculator etc. is not allowed for the students appearing for the test. All calculations / written work should be done in the rough sheet is provided with Question Paper.

Physics Section A Q. 1. P =

 az  a exp  −  b  K Bθ 



q → Temperature



P → Pressure



KB → Boltzmann constant



z → Distance



Dimension of b is

(1) [M0 L0 T0]

on the sphere and a horizontal force F is applied on the sphere as shown. If the particle does not slip on the sphere then the value of force F is : m

M R

θ

F

(2) [M–1L1T2]

(3) [M0L2T0] (4) [ML–1T–2]   Q. 2. If a1 and a2 are two non collinear unit   vectors and if | a1 + a 2 | = 3 , then the value     of ( a1 − a 2 ) . (2 a1 + a 2 ) is : 3 (1) 2 (2) 2 1 (3) (4) 1 2 Q. 3. A body is thrown from a point with speed 50 m/s at an angle 37° with horizontal. When it has moved a horizontal distance of 80 m then its distance from point of projection is : (1) 40 m

(2) 40 2 m

(3) 40 5 m

(4) None

Q. 4. A smooth sphere of radius R and mass M is placed on the smooth horizontal floor. Another smooth particle of mass m is placed

O

(1) F = mg cot q (2) F = Mg cot q (3) F=(m + M)g cot q (4) F =(m + M)g tan q Q. 5. A block of mass m is pulled by a constant power P placed on a rough horizontal plane. The friction co-efficient between the block and the surface is m. Maximum velocity of the block will be : µmg µP (1) (2) P mg P (3) mmgP (4) µmg Q. 6. 80 gm of water at 30°C is poured on a large block of ice at 0°C. The mass of ice that melts is : (1) 160 gm

(2) 80 gm

(3) 40 gm

(4) 30 gm

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Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 7. At NTP the density of a gas is 1.3 kg/m3 and the velocity of sound propagation in the gas is 330 m/s. The degree of freedom of gas molecule is : (1) 3 (2) 5 (3) 6 (4) 7 Q. 8. An expansion process on a diatomic ideal gas (Cv = 5/2 R), has a linear path between the initial and final coordinates on a pV diagram. The coordinates of the initial state are : the pressure is 300 kPa, the volume is 0.08 m3 and the temperature is 390 K. The final pressure is 90 kPa and the final temperature is 320 K. The change in the internal energy of the gas, in SI units, is closest to : (1) –11, 000 (2) –6500 (3) 11, 000 (4) zero Q. 9. A ring consisting of two parts ADB and ACB of same conductivity K carries an amount of heat H. The ADB part is now replaced with another metal keeping the temperatures T1 and T2 constant. The heat carried increases to 2H. What should be the conductivity of ACB the new ADB part ? (Given = 3) ADB C

T1

B

A D

T2

7 (1) K (2) 2 K 3 5 (3) K (4) 3 K 2 Q. 10. The height of mercury column measured with brass scale at temperature T0 is H0. What height H’ will the mercury column have at T = 0°C. Coefficient of volume expansion of mercury is g. Coefficient of linear expansion of brass is a : H 0 (1 + 3aT0 ) (1) H0(1 + aT0) (2) 1 + γT0 H 0 (1 + 3aT0 ) (3) (1 + γ / 3)T0

(4)

H 0 (1 + aT0 ) 1 + γT0

Q. 11. Two closed end pipes when sounded together produce 5 beat per second. If their length are in the ratio 100 : 101, then fundamental notes produced by them are : (1) 245, 250 (2) 250, 255 (3) 495, 500 (4) 500, 505 Q. 12. The period of rotation of the sun at its equator is T and its radius is R. Then the Doppler wavelength shift expected for light with wavelength l emitted from the edge of the sun’s disc is : [c = speed of light] πRl Tl (1) ± (2) ± cT 2 πRc 2 πRl 2 πRc (3) ± (4) ± cT Tl Q. 13. A plano convex lens has diameter of 10 cm and its thickness at the centre is 0.5 cm. Speed of light in the lens is 2 × 108 ms–1. What is the focal length of the lens ?

(1) 10 cm (2) 17.5 cm (3) 10.5 cm (4) 21 cm Q. 14. Parallel rays striking a spherical mirror far from the optic axis are focussed at a different point than are rays near the axis thereby the focus moves toward the mirror as the parallel rays move toward the outer edge of the mirror. What value of incidence angle q produces a 2% change in the location of the focus, compared to the location for q very close to zero ? (1) 3.5° (2) 5.5° (3) 8.5° (4) 11.5° Q. 15. A horizontal ray of light passes through a prism of index 1.50 and apex angle 4° and then strikes a vertical mirror, as shown in the figure (a). Through what angle must the mirror be rotated if after reflection the ray is to be horizontal ?

271

Mock Test Paper-11

(1) the intensity of the source is increased

prism mirror

(2) the exposure time is increased (3) the intensity of the source is decreased

4º

(4) the exposure time is decreased

Section B Fig. (a) (1) 1° (2) 2° (3) 2.5° (4) 1.5° Q. 16. Two plane mirrors are inclined at an angle of 40°. The possible number of images of an object placed at point P would be ?

Q. 21. A particle of mass 10–2 kg is moving along the positive x-axis under the influence of a force F(x) = -

K (2 x )2

where K = 10–2 Nm2.



At time t = 0 it is at x = 1.0 m and



its velocity is v = 0.



The velocity of partical will be .......... m/s, when it reaches x = 0.50 m.

Q. 22. A small bead of mass m can move on a smooth (1) 4 (2) 6 (3) 7 (4) 8 Q. 17. According to Bohr model, magnetic field at centre (at the nucleus) of a hydrogen atom due to motion of electron in the ninth orbit is proportional to : 1 (1) n3

(2)

1 n5

(3) n5 (4) n3 Q. 18. If la, lb and lc represent the Ka, Kb and La transition wavelengths in a hydrogen atom, respectively. Then which of the following is correct ? 1 1 1 1 1 1 (1) + = = (2) l A l B lC lC l B l A 1 1 1 1 1 1 (3) + = + = (4) l lC l B l lC l A B A Q. 19. One centimetre on the main scale of vernier callipers is divided into ten equal parts. If 10 divisions of vernier scale coincide with 8 small divisions of the main scale, the least count of the callipers is : (1) 0.005 cm (2) 0.05 cm (3) 0.02 cm (4) 0.01 cm Q. 20. The photocurrent in an experiment on photoelectric effect increases if :

circular wire (radius R) under the action of a force F =

Km r2

directed (r = position of bead

from P and K = constant) towards a point P within the circle at a distance R/2 from the centre. The minimum velocity should be .......... m/s of bead at the point of the wire nearest the centre of force (P) so that bead will complete the circle (Take

k = 8 unit) 3R

F O P R R/2

Q. 23. A disc of radius 5 cm rolls on a horizontal surface with linear velocity v = 1 ˆi m/s and angular velocity 50 rad/s. Height of particle from ground on rim of disc which has velocity in vertical direction is .......... cm. ω

y v

x

272

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 24. A container consist of hemispherical shell of radius ‘r’ and cylindrical shell of height ‘h’ radius of same material and thickness. The maximum value h/r so that container remain stable equilibrium in the position shown (neglect friction) is .......... .

Q. 27.



h

r Q. 25. An ideal fluid is flowing in two pipes of same cross-sectional pipes area. Both the pipes are connected with two vertical tubes, of length h1 and h2 as shown in figure. The flow is stream line in both pipes. If velocity of fluid at A, B, and C are 2 m/s, 4 m/s and 4 m/s respectively, the velocity of fluid at D (in m/s) is .......... .   C vA vC A • •

 vB • B

h1

h2 • D

 vD

Q. 26. A beam of charged particles accelerated using a potential difference of 5000 V falls to rest on a metal plate normally constituting a current of 500 mA. The force exerted by the beam on the plate is .......... × 10–6 N. (specific charge = 4 × 106 C kg–1 for each particle).

We have an infinite ladder of parallel resistances. what is the current through the circuit ? Q. 28. A DC supply of 120 V is connected to a large resistance X. A voltmeter of resistance 10 kW placed in series in the circuit reads 20 V. This is an unusual use of voltmeter for measuring very high resistance. The value of X is ……… kW (approx).

X

120V

10KΩ V

( ) K

Q. 29. A series LCR circuit containing a resistance of 120 W has angular resonance frequency 4 × 105  rads–1. At resonance the voltage across resistance and inductance are 60 V and 40 V respectively. The current in the circuit lags the voltage by 45° on the frequency of .......... ×105 rad/sec. Q. 30. 23Ne decays to 23Na by negative beta emission. Mass of 23Ne is 22.994465 amu mass of 23Na is 22.989768 amu. The maximum kinetic energy of emitted electrons neglecting the kinetic energy of recoiling product nucleus is ........ MeV.

Chemistry Section A Q. 31.

A0 atoms of X(g) are converted into X+(g) 2 A by absorbing energy E1. 0 ions of X+(g) 2 are converted into X–(g) with release of

energy E2. Hence ionization energy and electron affinity of X(g) are is : 2E1 2(E1 − E2 ) 2E1 2(E2 − E1 ) , , (1) (2) A0 A0 A0 A0 ( E1 − E2 ) 2E2 , (3) (4) None of these A0 A0

273

MOCK TEST PAPER-11 Q. 32.



1 8cm

Fig I





2

8cm

θ Fig II

In figure-I an air column of length l1, is entrapped by a column of Hg of length 8 cm. In figure-II length of same air column at the  same temperature is l2. The 1 is : 2 (1 atm = 76 cm of Hg)

2 2 (1) 1+ × cos q (2) 1 + × sin q 19 19 2 (3) 1+ × sin q 21

21 19

(4)

Q. 33. For which of the following KP is less than Kc? (1) N2O4  2NO2 (2) N2 + 3H2  2NH3 (3) H2 + I2  2HI (4) CO + H2O  CO2 + H2

1 Q. 34. Calculate pH of mixture of 400 ml of M 200 1 Ba(OH)2 400 ml of M HCl and 200 ml of 50 water :

(1) 8.4

(2) 2.1

(3) 2.8

(4) None of these

Q. 35. Write the IUPAC name of compound O CH3 – CH2 – C – CH – CH3 C=O CH3

(1) 3 - methyl hexane dione - 2, 4 - dione (2) 3 - ethyl hexane dione-2, 4 - dione (3) 1, 1-di ethyl hexane dione-2, 4 - dione (4) None of these Q. 36. The correct stereochemical name of CH3 H H C C CH2 C H C CH3 COOCH3

(1) Methyl 2-methylhepta (2E, 5E) dienoate (2) Methyl 2-methylhepta (2Z, 5Z) dienoate (3) Methyl 2-methylhepta (2E, 5Z) dienoate (4) Methyl 2-methylhepta (2Z, 5E) dienoate

Q. 37. 1000 g aqueous solution of CaCO3 contains 10 g of calcium carbonate. Hardness of the solution is : (1) 10 ppm (2) 100 ppm (3) 1000 ppm (4) 10000 ppm Q. 38. Boron reacts with nitric acid to form : (1) Sodium borate, H2 (2) Boric acid (3) Diborane (4) Borax Q. 39. What happens when steam is passed over red hot carbon : (1) C + 2H2 → CO2 + 2H2 (2) C + H2O → CO + H2 (3) Water vapour dissociates into H2 and O2 (4) None of these Q. 40. Halides of alkaline earth metals form hydrates such as MgCl2∙6H2O, CaCl2∙6H2O, BaCl2∙2H2O and SrCl2∙2H2O. This shows that halides of group 2 elements : (1) are hygroscopic in nature (2) can act as dehydrating agents (3) can absorb moisture from air (4) all of the above Q. 41. Which of the following is most stable carbocations : ⊕ ⊕ CH3 (1) (2) CH3– CH2 O CH

(3) CH3 – C ⊕

3



⊕

(4) CH3 – C – CH2

CH3 Q. 42. Which sodium salt will be heated with sodalime to obtain propane : (1) CH3 – CH2 – C – O–Na+ || O

(2) CH3 – CH2 –CH2 – C – O–Na+ || O

(CH3)2 – CH – C – O–Na+ (3) || O (4) 2 and 3 both Q. 43. The reaction of benzene with CO and HCl in the presence of anhydrous AlCl3 gives : (1) Chlorobenzene (2) Toluene (3) Benzyl chloride (4) Benzaldehyde

274

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 44. What are A and B in the following reaction Cl

(ii)CH3 CHO (i) Mg/Et 2 O Br  → B → A  (iii)aq.NH 4 Cl

CHOHCH3

MgCl

(1)

Br

& Cl

Cl

(2)

MgBr

&

CHOHCH3



MgCl

MgCl

(3)



Br

Br

&

CHOHCH3

(4) None of these Q. 45. A compound ‘X’ with molecular formula C3H8O can be oxidised to a compound ‘Y’ with the molecular formula C3H6O2, ‘X’ is most likely to be : (1) Primary alcohol (2) Secondary alcohol (3) Aldehyde (4) Ketone Q. 46. In the Cannizzaro reaction given below : – OH− → 2Ph–CHO  Ph–CH2OH + PhCO2 the slowest step is : (1) The attack of OH¯ at the carbonyl group (2)  The transfer of hydride to the carbonyl group (3)  The abstraction of proton from the carboxylic group (4) The deprotonation of Ph–CH2OH Q. 47. The relative order of reactivity of acyl derivatives is : O O O (1) R – C  –Cl > R –  C  – O – C  – R > O O R – C  – NH2 > R – C  – OR’ O

O

(2) R – C  –Cl > R – C  – OR’ > O

O

O

R– C  – O –  C  – R > R –  C  – NH2

O

O

O

(3) R –  C  – Cl > R –  C  – O – C  – R > O O R – C  – OR’ > R – C  – NH2 (4) None of the above Q. 48. Of the following statements : (P) C6H5N=CH–C6H5 is a Schiff ’s base (Q) A dye is obtained by the reaction of aniline and C6H5N=NCl (R) C6H5CH2NH2 on treatment with [NaNO2 + HCl] gives diazonium salt (S) p–Toluidine on treatment with [HNO2 + HCl] gives diazonium salt (1) Only (P) and (Q) are correct (2) Only (P) and (R) are correct (3) Only (R) and (S) are correct (4) (P), (Q) and (S) are correct Q. 49. When sucrose is heated with conc. HNO3 the product is : (1) Sucrose nitrate (2) Oxalic acid (3) Formic acid (4) Citric acid Q. 50. Kjeldahl’s method is used in the estimation of : (1) Nitrogen (2) Halogens (3) Sulphur (4) Oxygen

Section B Q. 51. An alloy of Iron (54.7%), nickel (45.0%) and manganese (0.3%) has a density of 8.17 g cm–3. .......... × 1026 iron atoms are there in a block of alloy measuring 10.0 cm × 20.0 cm × 15.0 cm. Q. 52. The wavelength associated with an electron equal to wavelength of proton would be .......... × 103. (mass of e = 9 × 10–28 g ; mass of proton = 1.6725 × 10–24 g) Q. 53. In following structure the percentage of ‘s’ character in lone pair occupy by oxygen atom is .......... .

275

MOCK TEST PAPER-11

F3 C Al

O θ

Al

CF3 CF3



F3 C



Given : Cos q =– 0.99

Q. 54. 4 m of pure A (d = 2.45 gm/m) was added 25.1 to 46 m of B (d = gm/m), the molarity 23 of solution of A in B will be .........., if density of final solution is 1.8 gm/m.

Given: Molar mass of A = 98.

Q. 58. On passing electricity through nitrobenzene solution, it is converted into azobenzene. The mass of azobenzene is .......... mg, if same quantity of electricity produces oxygen just sufficient to burn 96 mg of fullerene (C60). Q. 59. 0.1 mole of a gaseous compound B is mixed with 0.5 mole of solid A in a constant volume adiabatic bomb calorimeter in which A and B react according to reaction

3A (s) + 2B (g) → 3C (g) + 4D (l) : ∆H = ?



The temperature inside the calorimeter raise to 310 K from 300 K as a result of complete reaction.



The mixture of products now cooled back to original temperature at 300 K. Now a current of strength 100 mA flowing across a potential gradient of 10 Volt is passed for 1974 seconds through the calorimeter system which restores the temperature of product mixture to 310 K. The given reaction (calories) is [–)..........)J]. [Use R = 2 calories/ degree mole, 1 calorie = 4.2 Joule]

Molar mass of B = 46. Q. 55. 20% surface sites have adsorbed N2. On heating N2 gas evolved from sites and were collected at 0.001 atm and 298 K in a container of volume is 2.46 cm3. Density of surface sites is 6.023×1014/cm2 and surface area is 1000 cm2, the no. of surface sites occupied per molecule of N2 is .......... . Q. 56. The density of a pure substance ‘X’ whose atoms pack in cubic close pack arrangement is 1g/cc. If all tetrahedral voids are occupied by ‘Y’ atoms. The value of ‘3a’ is .......... g/cc, if the density of resulting solid is ‘a’ g/cc. [Given : Atomc mass (X) = 30 g/mol, (Y) = 20 g/mol] Q. 57. The vapour pressure of solution obtained by mixing 0.2 mol of NaCl in 72g of water at 25°C will be .......... torr.

[Given : vapour pressure of water at 25°C is 24.2 torr]

Q. 60. Enthalpy for the reaction Ag+ (aq) + Br¯ (aq) → AgBr(s) is – 84.54 kJ. Magnitude of enthalpy of formation of Ag+ (aq) and Br¯(aq) are in the ratio 8 : 9. Formation of Ag+(aq) is an endothermic process whereas formation of Br¯ is an exothermic process. Enthalpy of formation of AgBr is – 99.54 kJ/mol. The enthalpy of formation of Ag+ (aq) is .......... kJ/mol.

Mathematics Section A Q. 61. A circle touches two of the smaller sides of a ∆ABC (a < b < c) and has its centre on the greatest side. Then the radius of the circle is : a−b−c (1) 2

abc (2) 2

2∆ (3) a+b

a+b+c (4) 2

Q. 62. The number of solutions of the equation sin 2x – 2 cosx + 4 sinx = 4 in the interval [0, 5p] is : (1) 3

(2) 5

(3) 4

(4) 6

Q. 63. If |x – 1| + |x – 2| + |x – 3| ≥ 6 then. (1) 0 ≤ x ≤ 4

(2) x ≤ – 2 or x ≥ 4

(3) x ≤ 0 or x ≥ 4

(4) x ≤ – 1 or x ≥ 3

276

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 64. The value of ‘a’ for which the sum of the squares of the roots of 2x2 – 2(a – 2) x – a – 1 = 0 is least is 3 (1) 1 (2) 2 (3) 2 (4) –1 Q. 65. The sum of infinite number of terms of a decreasing G.P. is 4 and the sum of the 16 squares of its terms to infinity is , then the 3 G.P is : 1 1 1 1 1 (1) 2, 1, ,…. (2) , ,…… 2, 4 2, 4 8 1 1 1 4 , 8 , 16 ....... th Q. 66. The 4 term from the end in the expansion 7 æ x3 2 ö - 2 ÷ is : of ç ç 2 x ÷ è ø 2 (1) 70x (2) 70x 6 (3) – 35x (4) –70x m +n m–n Q. 67. If P2 = 30, then (m, n) is   P2 = 90 and given by : (1) (7, 3) (2) (16, 8) (3) (9, 2) (4) (8, 2) Q. 68. The orthocentre of the triangle formed by the lines 4x – 7y +10 = 0, x + y = 5 and 7x + 4y = 15, is : (1) (1, 2) (2) (1, –2) (3) (–1, –2) (4) (–1, 2) Q. 69. Length of intercept made by line x + y = 2 on the circle x2 + y2 – 4x – 6y – 3 = 0 is : (3) 2, 4, 8, ….

2 23 (1)

(4)

(2)

23

46 (3) (4) 4 23 Q. 70. If the vertex = (2, 0) and the extremities of the latus rectum are (3, 2) and (3, –2) then the equation of the parabola is : (1) y2 = 2x – 4 (2) x2 = 4y – 8 (3) y2 = 4x – 8 (4) x2 = 2y – 4 Q. 71. If the chord through the points whose eccentric angles are a and b on the ellipse x2 y2 + =1 passes through the focus (ae, 0), a2 b 2 a b then the value of tan tan will be 2 2 e +1 e –1 (2) (1) e –1 e +1 e +1 (3) e–2

(4)

e-2 e +1

Q. 72. The hyperbola

x2

–

y2

= 1 passes through a b2 the point of intersection of the lines x –3 5 y = 0 and 5x – 2y = 13 and the length of its latus rectum is 4/3 units. The coordinates of its focus are : 2

(1) (± 2 10 , 1)

(2) (± 3 10 , 0)

(3) (± 2 10 , 0)

(4) (± 3 10 , 1)

Q. 73. Two vertical poles of heights, 20 m and 80 m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, From this horizontal plane is : (1) 15

(2) 18

(3) 12 5

(4) 16 3

Q. 74. If f(x) = x – 20x + 240 x, then f(x) satisfies :

(1)  It is monotonically decreasing everywhere

(2) It is monotonically decreasing on (0, ∞) (3) It is monotonically increasing on (–∞, 0)

(4)  It is monotonically increasing everywhere

Q. 75. Let f(x) = (x – a)n g(x) , where

g(n) (a) ≠ 0 ; n = 0, 1, 2, 3....then

(1) f(x) has local extremum at x = a,



when n = 3

(2) f(x) has local extremum at x = a; when n = 4

(3)  f(x) has neither local maximum nor local minimum at x = a, when n = 2



(4)  f(x) has neither local maximum nor local minimum at x = a, when n = 4

Q. 76. If (x + iy)1/5 = a + ib, and u = (1) a – b is a factor of u

x y - , then a b

(2) a + b is a factor of x (3) a + ib is a factor of y (4) a – ib is a factor of a Q. 77. A line passes through the points (6, – 7, –1) and (2, –3, 1). The direction cosines of the line so directed that the angle made by it with positive direction of x-axis is acute, are : 2 -2 -1 (1) , , 3 3 3

(2)

2 -2 1 , , 3 3 3

2 2 1 (3) , , 3 3 3

(4) –

2 2 1 , , 3 3 3

277

Mock Test Paper-11    Q. 78. For three vectors u , v , w which of the following expressions is not equal to any of the remaining three ?       u . ( v × w ) (1) (2) ( v × w ) . u       v . (u × w ) (3) (4) ( u × v ) . w

é1 2 ù 2 Q. 79. If A = ê ú and A – kA – I2 = 0, then value 2 3 ë û of k is : (1) 4 (2) 2 (3) 1 (4) – 4 Q. 80. The value of the determinant

1 cos(b - a ) cos( g - a ) cos( a - b) 1 cos( g - b) cos( a - g ) cos(b - g ) 1

is equal to (1) cos a + cos b + cos g (2) cos a cos b + cos b cos g + cos g cos a (3) –1 (4) 0

Section B Q. 81. A complex number z is moving on æ z -1 ö p arg ç ÷ = . If the probability that è z +1ø 2 æ z3 - 1 ö p m arg ç 3 = is , where m, n ∈ prime, ç z + 1 ÷÷ 2 n è ø then (m + n) is equal to .......... æ 5k ö ÷ k where k = 5 + 1 Q. 82. Let tan 9° = ç 1 ç m ÷ è ø then m is equal to .......... Q. 83. Number of values of x which satisfy then 24 tan x + 12 sin2 x – relation 12 tan 2 x + 3 12 sin x + 7 in (–2p, 4p) ..........

Q. 84. Let

x 1,

x2,

x3

be

the

solutions

of

æ 2x + 1 ö æ 2x - 1 ö = 2 tan–1(x + 1) tan -1 ç + tan -1 ç ÷ ÷ è x +1 ø è x -1 ø

where x1< x2 2.00

If k = 0.5 J then the speed of this block as it crosses the patch is (use ln 20 = 3)

282

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

(1) 2.65 m/s (2) 1 m/s (3) 1.5 m/s (4) 2 m/s Q. 14. A triatomic molecule can be modelled as three rigid sphere joined by three rigid rods forming an triangle. Consider a triatomic gas consisting such molecule. If gas performs 30 J work when it expands under constant pressure the heat given to gas is : (1) 60 J (2) 30 J (3) 45 J (4) 120 J Q. 15. Wein’s constant is 2892 × 10–6 SI unit and the value of lm for moon is 14.46 micron. The surface temperature of moon is : (1) 100 K (2) 300 K (3) 400 K (4) 200 K Q. 16. A wave of frequency u = 1000 Hz, propagates at a velocity v = 700 m/sec along x-axis. Phase difference at a given point x during a time interval Dt = 0.5 × 10–3 sec is : (1) –p (2) p/2 (3) 3p/2 (4) 2p Q. 17. A ray of light when incident upon a thin prism suffers a minimum deviation of 39°. If the shaded half portion of the prism is removed, then the same ray will :

(1) suffer a deviation of 19.5° (2) suffer a deviation of 39° (3) not suffer any deviation (4) will be totally internally reflected Q. 18. A particle is dropped along the axis from a height 15 cm on a concave mirror of focal length 30 cm as shown in figure. The acceleration due to gravity is 10 m/s2. Find the maximum speed of image in m/s : 15cm

(1) 1.2 m/s (3) 2.25 m/s

(2) 3.5 m/s (4) 5.5 m/s

Q. 19. A Daniel cell is balanced on 125 cm lengths of a potentiometer wire. Now the cell is short circuited by a resistance 2 W and the balance is obtained at 100 cm. The internal resistance of the Daniel cell is (1) 0.5 W

(2) 1.5 W

(3) 1.25 W

(4) 4/5 W

Q. 20. Consider the following circuit :



The potential drop across the 20 kΩ resistor would be :

(1) 4V

(2) 3V

(3) 5V

(4) 2V

Section B Q. 21. A particle moves in a straight line with its retardation proportional to its displacement ‘x’. Change in kinetic energy is proportional to nth power of x, where n is .......... Q. 22. The minimum radius of a circle along which a cyclist can ride with a velocity 18   km/hr if the coefficient of friction between the tyres and the road is m = 0.5, is .......... (Take g = 10 m/s2) Q. 23. Machine gun mounted on car is firing 30 bullets per minute onto the truck moving with speed 90 km/hr. The car is chasing truck with speed 180 km/hr. Numbers of bullet hitting the truck per min is .......... (Speed f bullet with respect to ground = 300 m/s) Q. 24. A disc of mass M and radius R is placed a rough horizontal surface with its axis horizontal. A light rod of length ‘2R’ is fixed to the disc at point ‘A’ as shown in figure 3 and a force Mg is applied at the other 2 end. If disc starts to roll without slipping the value of ‘’10×mmin’’ where mmin is minimum coefficient of friction between disc and horizontal surface required for pure rolling is ..........

283

MOCK TEST PAPER-12 2R

3 Mg 2

R/2 R

Q. 25. A ball is immersed in water kept in container and released. At the same time container is accelerated in horizontal direction with acceleration, 44 m /s 2 . Acceleration of ball w.r.t. container is .......... m/s2 (specific gravity of ball = 12/17, g = 10 m/s2) : Q. 26. A glass capillary sealed at the upper end is of length 0.11 m and internal diameter 2 × 10–5 m. This tube is immersed vertically into a liquid of surface tension 5.06 ×10–2 N/m. When the length x × 10–2 m of the tube is immersed in liquid then the liquid level inside and outside the capillary tube becomes the same, then the value of x is .......... m. (Assume atmospheric N pressure is 1.01 × 105 2 ) m

Q. 27. The shortest wavelength of the Brackett series of a hydrogen like atom of atomic number Z is same as the shortest wavelength of the Balmer series of hydrogen atom, then the value of Z is .......... Q. 28. In U238 ore containing Uranium the ratio of U234 to Pb206 nuclei is 3. Assuming that all the lead present in the ore is final stable product of U238. Half life of U238 to be 4.5 × 109 years and the age of ore is .......... × 109 years. (in 109 years) Q. 29. The De-Broglie wavelength of electron in the third Bohr orbit of hydrogen is .......... × 10–11 m (given radius of first Bohr orbit is 5.3 × 10–11 m) : Q. 30. The wavelength of light incident on a metal surface is reduced from 300 nm to 200 nm (both are less than threshold wavelength). What is the change in the stopping potential for photoelectrons emitted from the surface will be ...... V. (Take h = 6.6 × 10–34 J-s)

Chemistry Section A Q. 31. NH3 and BF3 combine readily because of the formation of : (1) a covalent bond

(1) CH2(OH)CH2COOH and CH3–CH(OH)COOH (2) C2H5OH and CH3OH (3) (C4H5)2CO and CH3COOCH2CH2CH3 (4) All of the above

(2) a hydrogen bond (3) a co-ordinate bond (4) an ionic bond Q. 32. If there were 10 periods in periodic table then maximum number of elements it can have is : (1) 290

(2) 770

(3) 204

(4) None of these

Q. 33. In the trivial system which prefix will be used for the following compound ? CH3 CH3 C CH3

Q. 35. The volume of ‘10 Vol’ of H2O2 required to liberate 500 mL O2 at NTP is : (1) 50 mL

(2) 25 mL

(3) 100 mL

(4) 125 mL

Q. 36. On the addition of mineral acid to an aqueous solution of borax, the compound formed is : (1) Orthoboric acid (2) Boron hydride (3) Metaboric acid

(4) Pyroboric acid

Q. 37. On heating graphite with conc. HNO3 repeatedly, a yellow mass is obtained which is called :

(1) Neo

(2) Tertiary

(1) Graphitic oxide

(3) Secondary

(4) Iso

(2) Graphitic peroxide

Q. 34. Which one of the following pairs are called position isomers :

(3) Benzene hexacarboxylic acid (4) Graphitic nitrate

284

Oswaal JEE (Main) Mock Test 15 Sample Question Papers ∆

→ (1) Q. 38. BaC2 + N2  ∆ → (2) CaC2 + N2  (1) and (2) are : (1) BaCN2, CaCN2 (2) Ba(CN)2, Ca(CN)2 (3) Ba(CN)2, CaCN2 (4) None is correct Q. 39. Consider the following carbocations (a) ⊕ CH2 CH3O

(b) (c)

⊕ CH2

CH3

⊕ CH2

(d) CH3 — ⊕ CH2

The relative stabilities of these carbocations are such that : (1) d < b < c < a (2) b < d < c < a (3) d < b < a < c (4) b < d < a < c Q. 40. Consider the reaction CH3 ⊕| Heat CH3CH2CH2–N–CH2CH3 OH– | CH 3 Which of the following is formed in major amount ? (1) CH2 = CH2 (2) CH3CH = CH2 (3) Both (1) and (2) in equal amount (4) None, as no reaction takes place Q. 41. Consider the following statements about benzene: I : Heats of hydrogenation of benzene and 1, 3, 5-cyclohexatriene are identical II : Benzene is much more stable than expected for 1, 3, 5-cyclohexatriene III : All carbon-carbon bonds (single and double) have equal length Select correct statements : (1) I, II (2) II, III (3) I, III (4) I, II, III Q. 42. C2H5Cl + AgF → C2H5F + AgCl The above reaction is called :

(1) Hunsdiecker (2) Swart (3) Strecker (4) Wurtz Q. 43. Propene, CH3 – CH = CH2 can be converted to 1-propanol by oxidation. Which set of reagents among the following is ideal to effect the conversion : (1) Alkaline KMnO4 (2) B2H6 and alkaline H2O2 (3) O3 /Zn dust (4) OsO4 / NaHSO3 Q. 44. For distinction between CH3CHO and C6H5CHO the reagent used is : (1) KCN (2) HCN (3) NH2OH (4) PCl5 red P

LiAlH

4  CH3COOH  → Y. Q. 45. X ← HI What does NOT true for X and Y : (1)  X is hydrocarbon of general formula CnH2n+2 while Y belong to alkanol (2) X can be obtained by reducing CH3CH2Cl while Y by its hydrolysis (3) X gives positive litmus test but Y does not (4)  X and Y both belong to different homologeous series Q. 46. Identify ‘Z’ in the reaction given below : NH2

1.HNO2(280K) NaOH CH3I Y Z 1.H2O; Boil X



NH–CH3 CH3

(1) H3C

CH3 N2Cl

(2) H3C

CH3

CH3

(3)

OCH3

OCH3

(4) OH

OH OH

285

MOCK TEST PAPER-12 Q. 47. Lassaigne’s test for the detection of nitrogen fails in : (1) NH2 CONHNH2. HCl (2) NH2NH2.HCl (3) NH2CONH2 (4) C6H5NHNH2.HCl Q. 48. Among the following ions, which one has the highest paramagnetism ? (1) [Cr(H2O)6]3+ (2) [Fe(H2O)6]2+ (3) [Cu(H2O)6]2+ (4) [Zn(H2O)6]2+ Q. 49. In blast furnace, the hearth is lined with (1) Dolamite refractories (2) Alumina refractories (3) Chromite refractories (4) Carbon refractories Q. 50. Ca, Ba and Sr ions are precipitated in fifth group as their : (1) Oxides (2) Sulphates (3) Carbonates (4) Sulphides

atoms. In one such experiment, one gram of silicon is taken and the boron atoms are found to be 1000 ppm by weight, when the density of the Si crystal decreases by 12%. The percentage of missing vacancies due to silicon, which are filled up by boron atoms will be .......... g. [Given : Atomic wt. Si = 30, B = 11] Q. 54. A solution is prepared by mixing 250 ml toluene (C7H8) and 8.4 g thiophene (C4H4S). Then molality of thiophene in the solution is .......... . [Given : Density of toluene = 0.8 g/ml, Density of thiophene = 1.2 g/ml]

Section B

Q. 56. Consider an isothermal cylinder and massless piston assembly in which ideal gas is filled. Cross sectional area of the cylinder = 1m2. Three masses m1, m2 and m3 are kept on the piston. When m1 is removed, piston moves upto point A. When m1 and m2 both are removed piston moves upto point B and when m1, m2 and m3 all the three are removed, piston moves upto point C. The work done by the gas is .......... J, when piston moves from point B to point C.

Q. 51. For a chemical reaction starting with some initial concentration of reactant At as a function of time (t) is given by the equation, 1 = 2 + 1.5 × 10–3 t 4 At

The rate of disappearance of [A] is .......... × 10–2 M/sec when [A]= 2 M. [Given : [At] in M and t in sec. ] [Express your answer in terms of 10–2 M /s] [Round off your answer if required] Q. 52. For adsorption of gas over solid surface following data is obtained at 300 K. Pressure of gas (mm of Hg)

100

25

Amount adsorged per kg of charcoal

3 gm

1.5 gm



[Multiply your answer by 10]

Q. 55. If the value of Ksp for Hg2Cl2 (s) is X then the value of X will be .......... where pX = – log X. Given :

Hg2Cl2 (s) + 2e– → 2Hg (l) + 2Cl–



E° = 0.27 V

Hg



+2

–

+ 2e → 2Hg (l)

E° = 0.81 V

[Given : m1 = 2 × 104 kg, m2 = 3 × 104 kg, g = 10 m/s2 ] Patm = 105 Pa

C B A

m1 m2

m3



The slope of the graph between log P vs log x/m will be .......... [x/m and P are in same units as given in question.] Q. 53. A strong current of trivalent gaseous boron passed through a silicon crystal decreases the density of the crystal due to part replacement of silicon by boron and due to interstitial vacancies created by missing Si

Pgas =106 Pa



V= 4 lit.

Q. 57. It is found that in 11.2L at 0°C and 1 atm, of any gaseous compound of ‘X’, there is never less than 15.5 gm of ‘X’. It is also found that 11.2 L of vapours of ‘X’ at 0°C and 1 atm, weighs 62 gm. The atomicity of ‘X’ is ..........

286

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 58 The de Broglie’s wavelength of electron emitted by a metal will be .......... Å whose threshold frequency is 2.25 × 1014 Hz when exposed to visible radiation of wavelength 500 nm. Q. 59. A 50 L gas stream was passed through a solution containing Cd2+ where H2S(in gas stream) was retained as CdS. The mixture was acidified and treated with 50 ml of 0.004 M I2. After the reaction S2– + I2 → S(s) + 2I– was complete, the excess iodine was treated with 15 ml of 0.01 M thiosulphate. The

concentration of H2S in ppm will be .......... . Use density of gas stream = 1.7 gm / L. [Divide your answer by 10] Q. 60. Enthalpy for the reaction Ag+ (aq) + Br¯ (aq) → AgBr(s) is : 90 kJ. Magnitude of enthalpy of formation of Ag+ (aq) and Br¯(aq) are in the ratio 5 : 6. Formation of Ag+(aq) is an endothermic process whereas formation of Br¯ is an exothermic process. Enthalpy of formation of AgBr is– 110 kJ/ mol. The enthalpy of formation of Ag+ (aq) will be .......... kJ/mol.

Mathematics Section A Q. 61. The statement p → (q → p) is equivalent to : (1) p → q (2) p → (p ∨ q) (3) p → (p → q) (4) p → (p ∧ q) Q. 62. Set of values of x satisfying the inequality

( x − 3)2 (2 x + 5)( x − 7) ( x 2 + x + 1)(3x − 6)2

≤ 0 is [a, b) ∪ (b, c]

then 2a + b + c is equal to (1) 0 (2) 4 (3) 5 (4) 7 Q. 63. The roots of the equation (b + c)x2 – (a + b + c) x + a = 0

(a, b, c ∈ Q, b + c ≠ a) are :

(1) irrational and different (2) rational and different (3) imaginary and different (4) real and equal Q. 64. If in a geometric progression {an}, a1= 3, an= 96 and Sn = 189, then the value of n is : (1) 5

(2) 6

(3) 7

(4) 8

Q. 65. If the coefficients of (2r + 4)th, (r – 2)th terms in the expansion of (1 + x)18 are equal, then r is : (1) 4

(2) 6

(3) 8

(4) 3

Q. 66. There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are

with numbers in ascending or descending order is equal to : (1) 12C8 (2) 12P8 (3) 2 × 12P8 (4) 2 × 12C8 Q. 67. If the angle between the tangent t The circle x2 + 42 + 2x + 4y – 11 = 0 from p (3, 3) is a tan −1   where a and b are relatively prime b then the value of a – 3b is: (1) 15

(2) 0

(3) 13

(4) 8

Q. 68. The equation of a circle passing through (3, –6) and touching both the axes is : (1) x2 + y2 – 6x + 6y + 8 = 0 (2) x2 + y2 + 6x – 6y + 9 = 0 (3) x2 + y2 + 30x – 30y + 225 = 0 (4) x2 + y2 – 30x + 30y + 225 = 0 Q. 69. The centre of the circle passing through the point (0, 1) and touching the parabola y = x2 at the point (2, 4) is :  6 53   −53 16  , (1)  (2)  ,   5 10   10 5   3 16   −16 53  , (3)  ,  (4)   10 5   5 10  x2 y2 Q. 70. Let The ellipse 2 + 2 = 1 has latus sectum a b equal 8 units – if the ellipse passes through

(

)

5 , 4 Then The radius of the directive

circle is (1) 5 3

(2) 3 5

(3)

(4) 15

15

287

MOCK TEST PAPER-12 Q. 71. The equation of conjugate axis for the ( x + y + 1)2 ( x − y + 2)2 hyperbola – = 1 is : 4 9 (1) x + y + 1 = 0 (2) x – y + 2 = 0 (3) x = – 3/2

(4) x + y + 2 = 0 n

n

y x Q. 72. The curve   +   = 2, touches the line a   b y x + = 2 at the point (a, b) for n is equal to a b

(1) 1 (2) 2 (3) 3 (4) all non zero values of n Q. 73. If f(x) = x + cos x – a then (1) f(x) is an increasing function (2) f(x) is a decreasing function

Q. 78. How many matrices can be obtained by using one or more numbers from four given numbers : (1) 76 (2) 148 (3) 124 (4) 82    Q. 79. A , B and C are three  non coplanar  vectors,   then ( A + B + C ) . (( A + B ) × ( A + C )) is equal to    (1) 0 (2) [ A , B , C ]       (3) 2 [ A , B , C ] (4) – [ A , B , C ] Q. 80. A point moves in such a way that sum of squares of its distances from the co-ordinate axis is 36, then distance of then given point from origin are : (1) 6 (2) 2 3 (3) 3 2 (4) 6

(3) f(x) = 0 has one positive root for a < 1

Section B

(4) f(x) = 0 has no positive root for a > 1 Q. 74. The set of values of p for which the points of extremum of the function

f(x) = x3 – 3px2 + 3 (p2 – 1)x + 1 lie in the interval (–2, 4), is

(1) (– 3, 5)

(2) (– 3, 3)

(3) (– 1, 3)

(4) (– 1, 5)

value of b 2 is .......... Q. 83. The value of

Q. 75. The value of the expression

Q. 81. The maximum value of the expression 5cos a + 12sin α – 8 is equal to .......... π 11π 5π   − cot Q. 82. If b =  3 + cot + cot , then the 8 24 24  

 x3   sin x − x + 6  1 lim   is , x→0 x5   k   then k is....

1. (2 – w) . (2 – w2) + 2 . (3 – w) (3 – w2) + ....... + (n – 1) (n – w) (n – w2), where w is an imaginary cube root of unity is : 2

 n( n + 1)  (1)   2  

2

 n( n + 1)  (2)   –n 2  

2

2 2  n( n + 1)  (3)  + n (4) n ( n + 1) − n  2   2

Q. 76. A single letter is selected at random from the word ‘PROBABILITY’. The probability that it is a vowel is : 3 2 (1) (2) 11 11 4 7 (3) (4) 11 11 Q. 77. If the following equations

x+y–3=0



(1 + l) x + (2 + l) y – 8 = 0



x – (1 + l) y + (2 + l) = 0



are consistent then the value of l can be

(1) 1

(2) –1

(3) 0

(4) 2

Q. 84. Number of values of x satisfying the system of equations π sin −1 2 + e −2 x − 2 e − x + sec −1 1 − x 2 + x 4 = 2 1+ tan −1 x − 1 = 4 + cos x  is .......... (where and 5   [.] denotes greatest integer function) x +1 Q. 85. If ƒ : [0, 1] → [0, 1] is defined by ƒ(x) = 4 and

d 1 ((ƒ o ƒ o ƒ........o ƒ)( x= )) , m∈N ,     dx mn 1 n times

x=

2

then the value of ‘m’ is .......... 1 x 2 sin − x x Q. 86. If L = lim , then value of L x →∞ 1− | x | is ..........

288

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 87. A function y = ƒ(x) satisfies the differential dy + x 2 y = -2 x , ƒ(1) = 1 . The value equation dx of |ƒ”(1)| is .......... Q. 88. Let ƒ(x) = x +

x2 x3 x4 x5 + + + and 2 3 4 5

æ xö 1 = tan -1 ç e ÷ – + C, where C is 2x b ( è a ø e - 1) constant of integration, then value of a + b is equal to .......... Q. 90. Let ƒ be continuous periodic function with



3



g(x) = ƒ (x), then |g’’(0)| is ..........

Q. 89. If

ò

2e 5x + e 4 x - 4 e3x + 4 e 2 x + 2e x

( e 2 x + 4 )( e 2 x - 1)2

ò

period 3, such that ƒ ( x ) dx = 1 . Then the

–1

0

8

value of

dx

ò ƒ ( 2x ) dx is ..........

-4

Answers Physics Q. No.

Answer

Topic Name

Q. No.

Answer

Topic Name

1

(2)

Electrostatics

16

(1)

Sound

2

(3)

Capacitance

17

(1)

Prism

3

(1)

Current Electricity

18

(3)

Reflection at Curve Surface

4

(2)

Magnetic Effect of Current

19

(1)

Practical Physics

5

(1)

Magnetism

20

(1)

Semi-Conductor

6

(4)

Electromagnetic Induction

21

2.00

Work Energy and Power

7

(2)

Alternating Current

22

5.00

Circular Motion

8

(2)

Gauss’s Law

23

33.00

Conservation Law

9

(3)

Unit & Dimension

24

8

Rotational Motion

10

(2)

Vector

25

7.83

Fluid Mech

11

(2)

Projectile

26

0.01

Surface Tension

12

(1)

Newton’s Law of Motion

27

2.00

Atomic Structure

13

(2)

Friction

28

2.00

Radioactivity

14

(4)

Kinetic Theory of Gases

29

99.90

Matter Wave

15

(4)

Radiation

30

2.00

Photo Electric Effect

Chemistry Q. No.

Answer

31

(3)

32

Topic Name

Q. No.

Answer

Topic Name

Chemical Bonding

46

(3)

Nitrogen Containing

(1)

Periodic Table

47

(2)

Practical Chemistry

33

(2)

Classification and Nomenclature

48

(2)

Coordination Compound

34

(1)

Isomerism

49

(4)

Metallurgy

35

(1)

Hydrogen Sets Compound

50

(3)

Salt Analysis

36

(1)

p-Block- Boron

51

1.20

Chemical Kinetics

37

(3)

p-Block –Carbon

52

2.00

Surface Chemistry

38

(3)

s-Block

53

2.00

Solid State

39

(1)

General Organic Chemistry

54

5.00

Surface Chemistry

40

(1)

Hydrocarbon

55

6.00

Electrochemistry

41

(2)

Aromatic Compound

56

3200

Thermodynamics

289

Mock Test Paper-12 42

(2)

Halogen Derivatives

57

4.00

Mole Concept

43

(2)

Alcohol, Ether and Phenol

58

9.84

Atomic Structure

44

(1)

Carbonyl

59

5.00

Redox Reaction

45

(1)

Carboxylic Acid

60

100

Thermo Chemistry

Mathematics Q. No.

Answer

61

(2)

62

Topic Name

Q. No.

Answer

Topic Name

Mathematical Reasoning

76

(3)

Probability

(1)

Inequalities

77

(1)

Determinant

63

(2)

Quadratic Equations

78

(2)

Metrices

64

(2)

Progressions

79

(4)

Vectors

65

(2)

Binomial Theorem

80

(3)

Three Dimensional Geometry

66

(4)

Permutation and Combination

81

5.00

Trigonometric Ratios

67

(3)

Circles

82

6.00

Trigonometric Ratios

68

(4)

Circles

83

120

Limits

69

(4)

Parabola

84

1.00

Inverse Trigonometric Functions

70

(2)

Ellipse

85

4.00

Functions

71

(1)

Hyperbola

86

0.00

Limits

72

(4)

Tangent & Normal

87

1.00

Differentiation Equation

73

(1)

Monotonicity

88

1.00

Differentiation

74

(3)

Maxima and Minima

89

4.00

Indefinite Integration

75

(2)

Complex Numbers

90

4.00

Definite Integration



MOCK TEST PAPER 13 Time : 3 Hours

Total Marks : 300

General Instructions : 1. 2. 3. 4. 5. 6.

There are three subjects in the question paper consisting of Physics (Q. no. 1 to 30), Chemistry (Q. no. 31 to 60) and Mathematics (Q. no. 61 to 90). Each subject is divided into two sections. Section A consists of 20 multiple choice questions & Section B consists of 10 numerical value type questions. In Section B, candidates have to attempt any five questions out of 10. There will be only one correct choice in the given four choices in Section A. For each question 4 marks will be awarded for correct choice, 1 mark will be deducted for incorrect choice for Section A questions and zero mark will be awarded for not attempted question. For Section B questions, 4 marks will be awarded for correct answer and zero for unattempted and incorrect answer. Any textual, printed or written material, mobile phones, calculator etc. is not allowed for the students appearing for the test. All calculations / written work should be done in the rough sheet is provided with Question Paper.

Physics Section A Q. 1. If the units of length and force are increased four times, then the unit of energy will : (1) Increase 8 times (2) Increase 16 times (3) Decreases 16 times (4) Increase 4 times      Q. 2. If a and b are  two unit vectors and R = a + b and also if |R| = R, then : (1) R < 0 (2) R > 2 (3) 0 ≤ R≤ 2 (4) R must be 2 Q. 3. A body moving with uniform acceleration describes 4 m in third second and 12 m in the fifth second. The distance described in next three second is : (1) 100 m (2) 80 m (3) 60 m (4) 20 m Q. 4. For a projectile thrown into space with a 3v2 speed v, the horizontal range is . The 2g 2 v vertical range is . The angle which the 8g projectile makes with the horizontal initially is : (1) 15° (2) 30° (3) 45° (4) 60°

Q. 5. A chain of mass ‘M’ and length ‘L’ is put on a rough horizontal surface and is pulled by constant horizontal force ‘F’ as shown in figure.    Velocity of chain as it turns completely: (Coefficient of friction = m)

F 1

1

1

1

ìæ 2F ì æ F ö L ü2 ö ü2 - mg ÷ ý (1) í2 ç - mg ÷ L ý (2) íç ø 2þ ø þ îè M î èM ì æ 2F ìæ 4F ö ü2 ö L ü2 - mg ÷ L ý (4) íç - mg ÷ ý (3) í2 ç ø þ ø 2þ î èM îè M Q. 6. The earth’s radius is R and acceleration due to gravity at its surface is g. If a body of mass m is sent to a height of R/4 from the earth’s surface, the potential energy changes by : R R (1) mg (2) mg 3 4 R R (4) 3 mg (3) mg 16 5 Q. 7. A ball falling in a lake of depth 200 m shows a decrease of 0.1% in its volume. The bulk modulus of elasticity of the material of the ball is : (Take g = 10 m/s2) (1) 109 N/m2 (2) 2 × 109 N/m2 (3) 3 × 109 N/m2

(4) 4 × 109 N/m2

291

Mock Test Paper-13 Q. 8. A particle at the end of a spring executes simple harmonic motion with a period t1, while the corresponding period for another spring is t2. If the period of oscillation with the two springs in series is T, then : (1) T = t1 + t2 (2) T2 = t12 + t22 (3) T–1 = t1–1 + t2–1 (4) T–2 = t1–2 +t2–2 Q. 9. The figure shows two fish tank, each having ends of width 1 foot. Tank A is 3 feet long while tank B is 6 feet long. Both tanks are filled with 1 foot of water. SA = the magnitude of the force of the water on the end of tank A SB = the magnitude of the force of the water on the end of tank B BA = the magnitude of the force of the water on the bottom of tank A BB = the magnitude of the force of the water on the bottom of tank B. Using the notation given above, Which one of the following sets of equations below is correct for this situation ?

1ft 1ft 6ft 3ft (1) SA = SB and BA = BB (2) SA = 2SB and BA = BB (3) 2SA = SB and 2BA = BB (4) SA = SB and 2BA = BB Q. 10. Potential difference between the points B and E of the circuits is : B C2 C1 D A

C3

E

C4

V

(C 2 - C1 ) V (C 4 - C3 ) (2) V (1)

ì C 2 C 3 - C1 C 4 ü (3) í ýV î C1 + C 2 + C 3 + C 4 þ C1 C 4 - C 3 C 2 ü (4) ìí ýV î (C1 + C 2 )(C3 + C 4 ) þ

Q. 11. A plane mirror is moving with velocity 4 ˆi + 5 ˆj + 8 kˆ . A point object in front of the mirror moves with a velocity 3 ˆi + 4 ˆj + 5 kˆ. Here kˆ is along the normal to the plane mirror and facing towards the object. The velocity of the image is : (1) –3 ˆi – 4 ˆj + 5 kˆ (2) 3 ˆi + 4 ˆj + 11 kˆ (3) –3 ˆi – 4 ˆj + 11 kˆ (4) 7 ˆi + 9 ˆj + 11 kˆ Q. 12. An object O is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm. The place surface of the lens is silvered as shown in fig. The image is formed at a distance of Objected

Silvered

20 cm

(1) 60 cm to the right of the lens (2) 30 cm to the left of the lens (3) 24 cm to the right of the lens (4) 12 cm to the left of the lens Q. 13. A triangular prism of glass is shown in figure. A ray incident normally to one face is totally internally reflected. If q is 45°, then index of refraction of the glass is : T

I

q

(1) less than 1.41 (2) equal to 1.41 (3) greater than 1.41 (4) None of these Q. 14. The central fringe of the interference pattern produced by light of wavelength 6000 Å is found to shift to the position of fourth bright fringe after a glass plate of refractive index 1.5 is introduced in path of one of beams. The thickness of the glass plate would be : (1) 4.8 mm (2) 8.23 mm (3) 14.98 mm (4) 3.78 mm Q. 15. Protons and singly ionized atoms of U235 and U238 are passed in turn (which means one after the other and not at the same time) through a velocity selector and then enter a uniform magnetic field. The protons

292

Oswaal JEE (Main) Mock Test 15 Sample Question Papers describe semicircles of radius 10 mm. The separation between the ions of U235 and U238 after describing semicircle is given by :

(1) 60 mm

(2) 30 mm

(3) 2350 mm

(4) 2380 mm

Q. 16. In uranium (Z = 92) the K absorption edge is 0.107 Å and the Ka line is 0.126 Å, the wavelength of the L absorption edge is : (1) 0.7 Å

(2) 1 Å

(3) 2 Å

(4) 3.2 Å

Q. 17. Assuming that about 200 MeV of energy is released per fission of 92U235 nuclei, then the mass of U235 consumed per day in fission reactor of power 1 megawatt will be approximately : –2 (1) 10 g

(2) 1 g

(3) 100 g

(4) 10,000 g

Section B Q. 21. The maximum kinetic energy of the photoelectrons ejected will be .......... eV, when light of wavelength 350 nm is incident on a cesium surface. Work function of cesium = 1.9 eV. Q. 22. A man is throwing bricks of mass 2 kg onto a floor from a height of 2 m. Bricks reaches to floor with speed 2 10 m/s. Man throws 10 bricks in a minute. If power of man is W watt 3 W is equal to .......... W. then 10 Q. 23. A body starts moving from origin at t = 0 with a velocity of 5 ˆi in x-y plane under the

Q. 24.

Q. 18. The velocity at which the mass of a particle becomes twice its rest mass will be : (1)

2C 3

(2)

C 2

(3)

C 3 2

(4)

3C 4

Q. 25.

Q. 19. If lattice parameter for a crystalline structure is 3.6 Å, then atomic radius in fcc crystal in Å is : (1) 7.20 Å (2) 1.80 Å (3) 1.27 Å (4) 2.90 Å Q. 20. The given figure shows the waveforms for two inputs A and B and that for the output Y of a logic circuit. The logic circuit is :

Q. 26.

A



O

T1 T2 T3 T4

O

T1 T2 T3 T4

t

B



t

Y

Q. 27. O



T1 T2 T3 T4

(1) an AND gate

(2) an OR gate

(3) a NAND gate

(4) a NOT gate

t

action of force producing an acceleration of (3 ˆi + 2 ˆj ) m/s2, then y-co-ordinate is .......... m of body when x-co-ordinate is 84 m. A wheel rotating at same angular speed undergoes constant angular retardation. After revolution angular velocity reduces to half its initial value. It will make .......... revolution before stopping. Air separated from the atmosphere by a column of mercury of length h = 15 cm is present in a narrow cylindrical two soldered at one end. When the tube is placed horizontally the air occupies a volume 3 V1 = 240 mm . When it is set vertically with its open end upwards the volume of the air is V2 = 200 mm3. The atmospheric pressure during the experiment is 7n cm of Hg where n is single digit number. n will be .......... . An electric heater is used in a room of total wall area 137 m2 to maintain a temperature of +20°C inside it, when the outside temperature is –10°C. The walls have three different layers materials. The innermost layer is of wood of thickness 2.5 cm, the middle layer is of cement of thickness 1.0 cm and the outermost layer is brick 25.0 cm. The power of the electric heater will be .......... W. Assume that there is no heat loss through the floor and the ceiling. The thermal conductivities of wood, cement and brick are 0.125, 1.5 and 1.0 watt/m/°C respectively. Two equal point charges of same sign are fixed on y-axis, on the either sides of the origin equidistant from it, distance between them d. A third charge moves along x axis. The distance of third charge from either of the two fixed charges when force on

293

Mock Test Paper-13 third charge is maximum will be .......... cm. [d = 10 cm] Q. 28. A capacitor has charge 50 mC. When the gap between the plates is filled with glass wool, then 120 mC charge flows through the battery to capacitor. The dielectric constant of glass wool is .......... . Q. 29. As a cell ages, its internal resistance increases. A voltmeter of resistance 270 Ω connected across an old dry cell reads 1.44 V. However,

a potentiometer at the balance point, gives a voltage measurement of the cell as 1.5 V. Internal resistance of the cell is .......... + 5.25 Ω. Q. 30. The mean lives of a radioactive substance are 1620 and 405 years for b-emission and b-emission respectively. The time after which three fourth of a sample will decay if it is decaying both by b-emission and b-emission simultaneously will be .......... years. (Take ln 2 = 0.693)

Chemistry Section A Q. 31. For the decomposition reaction NH2COONH4 (s) 2NH3 (g) + CO2 (g) –5 the KP = 2.9 × 10 atm3. The total pressure of gases at equilibrium when 1 mol of NH2COONH4(s) was taken initially could be : (1) 0.0194 atm (2) 0.0388 atm (3) 0.0582 atm (4) 0.0766 atm 1 1 M H2SO4, 400 ml of M HCl Q. 32. 400 ml of 100 200 and 200 ml water are mixed together, pH of the resulting solution is : (1) 2.1 (2) 2.8 (3) 3 (4) 3.1 Q. 33. Calculate the work involved when 1 mol of an ideal gas is compressed reversibly from 1.00 bar to 5.00 bar at a constant temperature of 300 K : (1) – 14.01 kJ (2) + 18.02 kJ (3) 4.01 kJ (4) – 8.02 kJ Q. 34. Write the IUPAC name of compound

SH CH3 – C – CH2 – SH CH2 – CH3 (1) 2 - methyl butane -1, 2 - di thiol (2) 3-methyl butane -1, 2 - di thiol (3) 1-ethyl-2-methyl butane -1, 2 - di thiol (4) 2-ethyl-1-methyl butane -1, 2 - di thiol Q. 35. Alkynes are isomers of : (1) Cycloalkane

(2) Alkadiene

(3) Alkene

(4) All of the above

Q. 36. Atomic hydrogen is obtained by passing ordinary hydrogen through : (1) A suitable catalyst maintained at high temperature under high pressure. (2) A solution containing zinc and sulphuric acid. (3) An electric arc. (4)  A silent electric discharge at ordinary temperature. Q. 37. When aqueous solution of AlCl3 concentrated, it furnishes crystals of : (1) Al2Cl6. 2H2O (2) AlCl3. 2H2O (3) Al2Cl6. 12H2O (4) Al2Cl6. 24H2O

is

Na2 CO3 H2O D ® (C). ® (A) ¾¾ ® (B) ¾¾¾¾ Q. 38. SiCl 4 ¾¾¾ heat The compound C is :

(1) SiO2

(2) Si

(3) SiC

(4) Na2SiO3

Q. 39. The decreasing order of the second ionization potential of K, Ca and Ba is : (1) K > Ca > Ba

(2) Ca > Ba > K

(3) Ba > K > Ca (4) K > Ba > Ca Q. 40. Which of the following is not paramagnetic : (1) Carbon free radical (2) Singlet carbene (3) Triplet carbene (4) All of the above Q. 41. What would be the main product when propene reacts with HBr in presence of benzoyl peroxide HH HH | | | | (1) CH3–C–C–H (2) CH3–C–C–H | | | | Br H H Br (3) Both A and B (4) Br–CH2–CH=CH2

294

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 42. In the following compounds : OH OH



CH3

(I)

(II) OH

OH



O (3) CH3 – CH2 – CH – CH2 OH OH (4) CH3 – CH2 – CH – CH2





(2) CH3CH2–C–CH3

NO2

NO2

(III)

(IV)

The order to acidity is :

(1) III > IV > I > II (2) I > IV > III > II (3) II > I > III > IV (4) IV > III > I > II Q. 43. A gem dichloride is formed in the reaction except : (1) CH3CHO and PCl5 (2) CH3COCH3 and PCl5 (3) CH2 = CH2 and Cl2 (4) CH2 = CHCl and HCl Q. 44. Which of the following reactions of alkanols does not involve C–O bond breaking : (1) CH3CH2OH + SOCl2 (2) CH3CH(OH)CH3 + PBr3 (3) CH3CH2OH + CH3COOH (4) ROH + HX Q. 45. Water soluble salt among AgNO3, AgF and AgClO4 are : (1) AgF, AgNO3 (2) AgF (3) AgF, AgNO3, AgClO4 (4) None of these Q. 46. Alkaline hydrolysis of C4H8Cl2 gives a compound (A) which on heating with NaOH and I2 produces a yellow precipitate of CHI3.The compound (A) should be. (1) CH3CH2CH2CHO

OH Q. 47. The oxidation of toluene with hot KMnO4 gives :

(1) Benzoic acid

(2) Benzaldehyde

(3) Benzene

(4) Benzyl alcohol

Q. 48. Which of the following compound cannot be produced if 1-propane amine is treated with NaNO2 and HCl : (1) Propane -1-ol (2) Propane-2-ol (3) 2-Chloropropane (4) 2-Propaneamine Q. 49. The destruction of the biological nature and activity of proteins by heat or chemical agent is called : (1) dehydration

(2) denaturation

(3) denitrogenation (4) deammination. Q. 50. A substance was known by its mode of synthesis to contain 10 atoms of carbon per molecule along with unknown number of atoms of chlorine hydrogen and oxygen. Analysis showed 60.5% carbon, 5.55% hydrogen, 16.10%j oxygen and 17.9% chlorine. The Empirical formula of the compound is : (1) C10H8OCl2

(2) C10H11O2Cl

(3) C10H10OCl

(4) C10H12O2Cl

Section B Q. 51. The spectral lines of atomic hydrogen wave number is equal to the difference between the wave numbers of the following two lines of the Balmer series : 486.1 and 410.2 nm? The wavelength of that line is .......... × 10– 4 cm. Q. 52. In a certain region of space there are only 5 molecules per cm3 on an average. The

295

Mock Test Paper-13 temperature is 3 K. The average pressure of this very dilute gas is .......... × 10–21 atoms. Q. 53. For a reaction: A(g) → nB(g) the rate constant is 6.93 × 10–4 sec–1. The reaction is performed at constant pressure and temperature of 24.63 atm and 300 K, starting with 1 mole of pure ‘A’. 3 M If concentration of ‘B’ after 2000 sec is 3.25 then the value of ‘n’ is .......... .



Q. 58. The net work done in the following cycle for one mol of an ideal gas will be .......... (in calorie), where in process BC, PT = constant. (R = 2 cal/mol-K).

B

Q. 54. In order to cause coagulation of 100 ml Arsenious sulphide sol 111.7 mg of 2 M NaCl solution is used, the coagulation value of NaCl will be .......... . Q. 55. The density of solid Argon is 1.6 ml at –233°C. If the Argon atom is assumed to be sphere of radius 1.5 × 10–8 cm, then the .......... % of solid Argon is apparently occupied.

[Take : NA = 6 × 1023, Atomic mass of Ar = 40]

Q. 56. Lauryl alcohol is obtained from coconut oil and is used to make detergent. A solution of 5 g of Lauryl alcohol in 200 g of benzene freezes at 4°C. The approximate molar mass of Lauryl alcohol will be .......... .

Given, Kf of benzene = 5.1°C/molal, Freezing point of benzene = 5.5°C.



[Give your answer after division by 17]

Q. 57. To produce 1,4-dicyanobutane following reduction is carried out :

2CH2 = CH–CN + 2H+ + 2e– → NC – (CH2)4 –CN

The current .......... (in Ampere) must be used to produce 162 g of 1,4-dicyanobutane per hour.

P

A 100



C 300 T(k)

400

Q. 59. 2 litre He gas at 2 atm and 300 K is inserted into a 4 litre rigid container containing N2 at 600K and 4 atm. Finally mixture is maintained at 600K temperature. The final pressure of gaseous mixture would be .......... torr. Q. 60. A gaseous mixture was passed at the rate of 2.5 L/min through a solution of NaOH for a total of 1 hour. The SO2 in the mixture was retained as sulphite ion : – SO2(g) + 2OH → SO32– (g) + H2O(l)



After acidification with HCl the sulphite was titrated with 5 ml of 0.003 M KIO3



IO3– + 2H2SO3 + 2Cl– → 2SO42– + ICl2– + 2H+ + H2O



The concentration of SO2 will be .......... ppm if density of gaseous mixture is 1.6 gm/L.

296

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Mathematics (3) a cos2a + b sin2a –

Section A Q. 61. If loga8 = g, logba = –1 and log1/4b = –1 then æ1 ö ç a + 1÷ è ø

log

5

( b2 + 4 g 2 )

is equal to :

(2) 5 (1) 5 (3) 25 (4) 625 Q. 62. If b and c are odd integers, then the equation x2 + bx + c = 0 has : (1) two odd roots (2) two integer roots, one odd and one even (3) no integer roots (4) two even roots Q. 63. The sum of n terms of an AP is 3n2 + 5n. The number of term which equals 164 is : (1) 13 (2) 21 (3) 27 (4) None of these n Q. 64. Let (5 + 2 6 ) = p + f where n ∈ N and p ∈ N and 0 < f < 1 then the value of f 2 – f + pf – p is (1) a natural number (2) a negative integer (3) a prime number (4) an irrational number Q. 65. There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is : (1) (2n + 2)! (2) (2n + 2)! × 2 (3) (n + 1)! × 2 (4) 2 ((n + 1)!)2 Q. 66. The coordinates of vertices of base BC of an isosceles triangle ABC are given by B (1, 3) and C (–2, 7) which of the following points can be the possible coordinates of the vertex A ? (1) (–7, 1/8) (2) (1, 6) (3) (–1/2, 5) (4) (–5/6, 6) Q. 67. The value of p so that the straight line x cos a + y sin a – p = 0 may touch the circle 2 2 2 2 x + y – 2ax cos a – 2by sin a – a sin a = 0 is :

a 2 – b 2 sin 2 a

2 2 2 2 2 (4) a cos a - b sin a + a - b sin a

Q. 68. The equation of the parabola whose vertex and focus are on the positive side of the x-axis at distances a and b respectively from the origin is 2 (1) y = 4(b – a) (x – a)

(2) y2 = 4(a – b) (x – b) 2 (3) x = 4(b – a) (y – a)

(4) x2 = 4(a – b) (y – b) Q. 69. The points where the normals to the 2 2 ellipse x + 3y = 37 are parallel to the line 6x – 5y = 2 are : (1) (4, 2) (– 5, – 2) (2) (5, 2) (– 5, – 3) (3) (5, 2) (– 5, – 2) (4) (5, –2) (–5, 2) Q. 70. The locus of the mid-point of the chords æ x2 ö æ y2 ö of the hyperbola ç 2 ÷ - ç 2 ÷ = 1 passing èa ø èb ø through a fixed point (a, b) is a hyperbola

a b with centre at æç , ö÷ It equation is : è 2 2ø

2

2

2

2

2

2

2

2

aö bö æ æ çx - ÷ çy- ÷ 2 2 2ø -è 2ø = a - b è (1) a2 b2 4 a2 4b 2 aö bö æ æ çx + ÷ çy- ÷ 2 2ø -è 2ø = a + b è (2) a2 b2 4 a2 4b 2 aö bö æ æ çx - ÷ çy- ÷ 2 2ø -è 2ø = a - b è (3)  a2 b2 4 a2 4b 2 æx + a ö æy+ bö ÷ ç ÷ (4) çè a b2 2ø 2ø è = a2 b2 4 a2 4b 2 Q. 71. The normals to the curve x = a (q + sin q), y = a (1 – cos q) at the points

q = (2n + 1) p, n ∈ I are all :

(1) parallel to x-axis (2) parallel to y-axis

(1) a cos a + b sin a – a + b sin a

(3) parallel to the line y = x

(2) a cos2a – b sin2a –

(4) parallel to the line y = –x

2

2

2

2

2

a 2 + b 2 sin 2 a

297

Mock Test Paper-13 2x Q. 72. Function f(x) = log (1 + x) – is 2+x monotonically increasing when : (1) x < 0 (2) x > 0 (3) x ∈ R (4) x > –1 Q. 73. A cone of maximum volume is inscribed in a given sphere. Then the ratio of the height of the cone to the diameter of the sphere is 3 1 (2) (1) 4 3 1 2 (3) (4) 4 3 Q. 74. In an equilateral triangle, the in-radius, circum-radius and one of the ex-radii are in the ratio : (1) 2 : 3 : 5 (2) 1:2:3 (3) 1 : 3 : 7 (4) 3:7:9 n

æ 1 + cos q + i sin q ö Q. 75. ç ÷ = è 1 + cos q - i sin q ø (1) cos nq + i sin nq (2) sin nq + i cos nq nq nq (3) cos + i sin 2 2 (4) cos nq

Section B Q. 81. Let y = ƒ(x) be a real- valued differentiable function on R (the set of all real numbers) such that ƒ(1) = 1. If ƒ(x) satisfies xƒ’(x) = x2 + ƒ(x) – 2, then the area bounded by ƒ(x) with x-axis between ordinates x = 0 and x = 3 is equal to .......... . Q. 82. If area of the region bounded by 2 2 y ³ cot ( cot -1 |ln| e|x| ) and x + y – 6|x| – 6|y| + 9 ≤ 0, is lp, then l is .......... .

é -2 1 ù 2 Q. 78. If A = ê ú Then 2 A – 3A : ë 0 3û é14 -1ù (1) ê ú ë0 9û

é -14 1 ù (2) ê ú ë 0 9û

é14 1 ù (3) ê ú ë 0 -9 û

é14 - 1ù (4) ê ú ë0 - 9 û

Q. 79. If A, B and C are the angles of a triangle ABC, then sin2A sinC sinB sinC sin2B sinA = sinB sinA sin2C (2) 1 (4) 3

ò (( cos 2t - 1) ( cos t - e x

Q. 83. If

Q. 76. The points A(5, –1, 1); B(7, –4, 7); C(1, –6, 10) and D(–1, –3, 4) are vertices of a : (1) square (2) rhombus (3) rectangle (4) trapezium  with the vector Q. 77. If the vector b is collinear   a = (2 2 , –1, 4) and | b | = 10, then       (1) a ± b = 0 (2) a ± 2 b = 0       (3) 2 a ± b = 0 (4) a ± 3 b = 0

(1) 0 (3) 2

Q. 80. A bag contains 20 tickets numbered 1 to 20. Two tickets are drawn at random. The probability that both the numbers on the ticket are prime is : 4 14 (2) (1) 95 95 17 9 (3) (4) 95 95

-t 2

0

) t ) dr -n

is a cos x - 1 finite non-zero number, Then the integer value for n is .......... .

Q. 84. If

Lt

x ®0

ò

x + (cos-1 3x )2 1 - 9x 2

dx

(

)

b 1 1 - 9 x 2 + ( cos-1 3x ) + C , a where C is constant of integration , then ( a + 3b ) is equal to .......... .

 =

Q. 85. Let a function y = ƒ(x) is defined by q sinq x = e sin q and y = qe , where q is a real parameter, then value of lim f ¢( x ) is .......... . q®0

Q. 86. Let ƒ : R → R be a polynomial function satisfying ƒ(x + y) = ƒ(x) + ƒ(y) + 3xy(x + y) f (2 x ) – 1 " x, y ∈ R and ƒ’(0) = 1, then xlim ®¥ f ( x ) is equal to .......... . Q. 87. If lim

x ®¥

a 1 æ px + 1 ö tan ç ÷ p b x +1 è 2x + 2 ø =

(a, b ∈ N); then the value of a + b is .......... . Q. 88. Let a and b are two positive integers such that b ≠ 1. Let g(a, b) = Number of lattice points inside the quadrilateral formed by lines x = 0, y = 0, x = b and y = a.

298

Oswaal JEE (Main) Mock Test 15 Sample Question Papers é a ù é 2a ù é ( b - 1)a ù , ƒ(a,b) = ê ú + ê ú + ... + ê ëbû ë b û ë b úû



é 5p ù Q. 89. If q Î ê , 3p ú and 2cos q + sin q = 1, then ë 2 û the value of 7cos q + 6sin q is .......... .

é g (101, 37) ù then the value of ê ú is .......... . ë f (101, 37) û



(Note P(x, y) is lattice point if x, y ∈ I) (where [.] denotes greatest integer function)

Q. 90. In a DABC, let BC = 3. D is a point on BC 2 such that BD = 2, Then the value of AB + 2AC2 – 3AD2 is .......... .

Answers Physics Q. No.

Answer

1

(2)

2

Topic Name

Q. No.

Answer

Topic Name

Unit & Dimension

16

(1)

X-Ray

(3)

Vector

17

(4)

Nuclear Physics

3

(3)

One Dimension

18

(3)

Matter Wave

4

(2)

Projectile

19

(3)

X-rays

5

(3)

Friction

20

(1)

Communication system

6

(3)

Gravitation

21

1.60

Photo electric Effect

7

(2)

Elasticity

22

1.33

Work Energy and Power

8

(2)

Surface tension

23

36.00

Conservation Law

9

(4)

Gauss Law

24

3.00

Rotational

10

(4)

Capacitance

25

5.00

Kinetic Theory of Gases

11

(2)

Reflaction at Plane and Curved Surface

26

9000

Heat Conduction

12

(4)

Refraction at Plane Surface

27

12.20

Electrostatics

13

(3)

Prism

28

2.40

Capacitance

14

(1)

Wave nature of Light-Interference

29

11.25

Current Electricity

15

(1)

Atomic Structure

30

449

Radioactivity

Chemistry Q. No.

Answer

31

(3)

32

Topic Name

Q. No.

Answer

Topic Name

Chemical Equilibrium

46

(2)

Carbonyl

(1)

Ionic Equilibrium

47

(1)

Carboxylic Acid

33

(3)

Chemical Energetics

48

(4)

Nitrogen Compound

34

(1)

IUPAC

49

(2)

Biomolecules

35

(2)

Isomerism

50

(2)

Practical Chemistry

36

(3)

Hydrogen Family

51

41.03

Atomic Structure

37

(3)

p-Block-Boron

52

2.04

Mole

38

(4)

p-Block –Carbon

53

4.00

Chemical Kinetics

39

(1)

s-Block

54

2.00

Surface Chemistry

40

(2)

General Organic Chemistry

55

3.00

Solid State

299

Mock Test Paper-13 41

(2)

Hydrocarbon

56

5.00

Solution

42

(4)

Aromatic

57

80.40

Electrochemistry

43

(3)

Halogen Derivatives

58

200

Thermodynamics

44

(3)

Alcohol, Phenol, Ether

59

4560

Gaseous State

45

(3)

Transition Element

60

8.00

Redox Reaction

Topic Name

Mathematics Q. No.

Answer

Topic Name

Q. No.

Answer

61

(4)

Logarithms

76

(2)

Three Dimensional Plane

62

(3)

Quadratic Equations

77

(3)

Vector

63

(3)

Progressions

78

(1)

Metrics

64

(2)

Binomial Theorem

79

(1)

Determinant

65

(4)

Permutation and Combination

80

(2)

Probability

66

(4)

Point & Straight Line

81

6.00

Differential Equation

67

(1)

Circle

82

9.00

Area under Curve

68

(1)

Parabola

83

3.00

Limits

69

(3)

Ellipse

84

0.00

Indefinite Integration

70

(1)

Hyperbola

85

0.00

Differentiation

71

(1)

Tangent & Normal

86

8.00

Continuity

72

(4)

Monotonic

87

3.00

Limit

73

(4)

Maxima and Minima

88

2.00

Function

74

(2)

Mathematical Reasoning

89

6.00

Trigonometric Ratio

75

(1)

Complex Number

90

6.00

Properties of Triangles



MOCK TEST PAPER 14 Time : 3 Hours

Total Marks : 300

General Instructions : 1. 2. 3. 4. 5. 6.

There are three subjects in the question paper consisting of Physics (Q. no. 1 to 30), Chemistry (Q. no. 31 to 60) and Mathematics (Q. no. 61 to 90). Each subject is divided into two sections. Section A consists of 20 multiple choice questions & Section B consists of 10 numerical value type questions. In Section B, candidates have to attempt any five questions out of 10. There will be only one correct choice in the given four choices in Section A. For each question 4 marks will be awarded for correct choice, 1 mark will be deducted for incorrect choice for Section A questions and zero mark will be awarded for not attempted question. For Section B questions, 4 marks will be awarded for correct answer and zero for unattempted and incorrect answer. Any textual, printed or written material, mobile phones, calculator etc. is not allowed for the students appearing for the test. All calculations / written work should be done in the rough sheet is provided with Question Paper.

Physics Section A Q. 1. The r.m.s. speed of a certain gas is v at 127°C K. The temperature at which the r.m.s. speed becomes two times, will be : (1) 527°C (2) 1327°C (3) 1227°C (4) None of these Q. 2. A force vector applied on a mass is represented  ˆ ˆ ˆ as F = 6i − 8 j + 10 k N and accelerates the mass at 1 m s–2. The mass of the body is : (1) 10 kg (2) 20 kg (3) 2 10 kg (4) 10 2 kg Q. 3. The displacement s of a particle depends on time t according to the following relation 1 s= t3 – t2 + t. The velocity and displacement 3 of the particle at the instant when its acceleration is zero, are respectively : 1 1 (1) 0, (2) , 0 3 3 1 1 (3) , (4) None of the above 3 3 Q. 4. A person standing on a truck moving with a uniform velocity 14.7 ms–1 on a horizontal road throws a ball in such a way that it returns to him after 4s. Find the speed and angle of projection as seen by a man on the road : (1) 19.6 ms–1, vertical (2) 24.5 ms–1, vertical

(3) 19.6 ms–1, 53° with the road (4) 24.5 ms–1, 53° with the road Q. 5. A force F is applied to the initially stationary cart. The variation of force with time is shown in the figure. The speed of cart at t = 5 sec is : 10 kg

F

50 F(N)

Parabolic

5 t(s) (1) 10 m/s (2) 8.33 m/s (3) 2 m/s (4) Zero Q. 6. The coefficient of static friction between a car’s tires and a level road is 0.80. If the car is to be stopped in a maximum time of 3.0 s, its speed cannot exceed (1) 2.4 m/s (2) 7.8 m/s (3) 2.6 m/s (4) 23.5 m/s Q. 7. An earthen pitcher loses 1 gm of water per minute due to evaporation. If the water equivalent of pitcher is 0.5 kg and pitcher contains 9.5 kg of water, calculate the time required for the water in pitcher to cool to 28°C from original temperature of 30°C. Neglect radiation effects. Latent heat of

301

MOCK TEST PAPER-14 vaporization in this range of temperature is 580 Cal/gm and specific heat of water is 1 Cal/gm°C. (1) 30.5 min (2) 41.2 min (3) 38.6 min (4) 34.5 min Q. 8. One mole of a gas expands obeying the relation as shown in P-V diagram. The maximum temperature in this process is equal to : P A P0

P0 2

B V0

(1)

P0 V0 R

2V0

(2)

V 3P0 V0 R

9P0 V0 (4) None of these 8R Q. 9. A system is taken through a cyclic process represented by a circle as shown. The heat absorbed by the system is :

(3)

π (1) p × 10 J (2) J 2 2 (3) 4p × 10 J (4) p J Q. 10. A metal ball immersed in water weighs w1 at 0°C and w2 at 50°C. The coefficient of cubical expansion of metal is less than that of water. Then : (1) w1 > w2 (2) w1 < w2 (3) w1 = w2 (4) data is insufficient Q. 11. Two perfectly identical wires kept under tension are in unison. When the tension in wire is increased by 1% then on sounding them together 3 beats are heard in 2 seconds. What is the frequency of each wire? (1) 300 Hz (2) 400 Hz (3) 256 Hz (4) 288 Hz Q. 12. A white light is incident at 20° on a material of silicate flint glass slab as shown. mviolet = 1.66 and mr = 1.6. For what value of d will the separation be 1 mm in red and violet rays. 3

20º

V air

air

R V d.

R

1mm 5 10 (1) cm (2) cm 3 3 20 (3) 5 cm (4) cm 3 Q. 13. Two concave refracting surfaces of equal radii of curvature face each other in air as shown in figure. A point object O is placed midway between the centre and one of the poles. Then the separation between the images of O formed by each refracting surfaces is : n = 1.5

n = 1.5

glass

glass

(1) 11.4 R

(2) 1.14 R

(3) 0.114 R

(4) 0.0114 R

Q. 14. In a young double slit apparatus the screen is rotated by 60° about an axis parallel to the slits. The slits separation is 3 mm, slit to screen distance (at central fringe) is 4 m, and wavelength of light is 450 nm. The separation between the third dark fringe on the either side of central fringe is : (1) 6 mm

(2) 8 mm

(3) 4 3 mm

(4) 2 3 mm

Q. 15. An electron in H-atom makes a transition from n = 3 to n = 1. The recoil momentum of H-atom will be : (1) 6.45 × 10–27 N s (2) 6.8 × 10–27 N s (3) 6.45 × 10–24 N s (4) 6.8 × 10–24 N s Q. 16. If 10% of a radioactive substance decays in every 5 years, then the percentage of the substance that will have decayed in 20 years will be : (1) 40%

(2) 50%

(3) 65.6 %

(4) 34.4 %

302

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 17. Which of the following is true for X-rays : (1)  wavelength of continuous X-rays does not depend on potential difference (2) wavelength of discrete X-rays does not depend on potential difference (3) discrete X-rays have energy of the order of MeV (4)  continuous X-rays have energy of the order of MeV Q. 18. We wish to observe an object which is 2.5 Å in size. The minimum energy photon that can be used : (1) 5 KeV (2) 8 KeV (3) 10 KeV (4) 12 KeV Q. 19. Two students measure the weight of a 10 Kg mass using a spring balance and record these readings as : A : 10Kg, 10Kg, 10.5Kg, 10.5Kg, 9.5Kg B : 10Kg, 10.1Kg, 10.1Kg, 9.8Kg, 9.9Kg Then (1) A and B both are equally precise (2) B is more accurate than A (3) Neither A nor B is accurate (4) B is more precise than A. Q. 20. What should be the minimum length of a tower to propagate a signal of 300MHz? (1) 100 cm (2) 50 cm (3) 25 cm (4) 12.5 cm

Section B Q. 21. The potential energy of a particle under a conservative force field is given by U = 10 + (x – 4)2, where x is in meter. At x = 6 m, K.E. of particle is 10 J. The maximum kinetic energy of particle is .......... J. Q. 22. Two blocks P and Q of masses 0.3 kg and 0.4 kg, respectively, are stuck to each other by some weak glue as shown in the figure. They hang together at the end of a spring with a spring constant k = 200 N/m. The block Q suddenly falls free due to failure of glue, then the maximum kinetic energy of the block P during subsequent motion will be .......... mJ.

Q. 23. A disc is rotating freely about its axis. Percentage change in angular velocity of disc if temperature decreases by 20°C is .......... (coefficient of linear expansion of material of –4 disc is 5 × 10 /°C ) Q. 24. A mercury pallet is trapped in a tube as shown in figure. The tube is slowly heated to expel all mercury inside it (Isothermal condition). Heat given to the tube is .......... (rHg = 13.6 gm/cc, Atmospheric pressure 5 2 = 10 Pa, cross–section area of tube = 2 cm ) 10 cm 5 cm 10 cm

Q. 25. A straight infinitely long cylinder of radius R0 = 10 cm is uniformly charged with a surface charge density s = + 10–12 C/m2. The cylinder serves as a source of electrons, with the velocity of the emitted electrons perpendicular to its surface. Electron 5 velocity must be .......... × 10 m/s to ensure that electrons can move away, from the axis of the cylinder to a distance greater than 3 r = 10 m. Q. 26. An isolated parallel plate capacitor is maintained at a certain potential difference. When a 3 mm thick slab is introduced between the plates, in order to maintain the same potential difference the distance between the plates is increased by 2.4 mm. The dielectric constant of slab will be .......... . Q. 27. Each resistance is of 2 W. Current in resistance R (R = 2 W) is …… + 9.75 A. 2W 50V 2W

2W

P Q

2W R

2W

2W

2W

2W i

i 100V

303

MOCK TEST PAPER-14 Q. 28. A charge particle of charge q and mass m is projected in a region which contains electric and magnetic field as shown in figure with velocity V at an angle 45° with x-direction. qE If V = , then net deviation in particle m motion will be (neglect the effect of gravity) in clockwise direction approx …….. °. y E

V

⊗B

45º

x

Q. 29. A light ray in medium (RI = 5/3) enters another medium at an angle 30°. The angle in other medium is sin–1 (5/6). The incident angle must be increased such that the ray is completely reflected at minimum degrees is .......... . Q. 30. A point isotropic light source of power P = 12 watts is located on the axis of a circular mirror of radius R = 3 cm. If distance of source from the centre of mirror is a = 39 cm and reflection coefficient of mirror is a = 0.70 then the force exerted by light ray on the mirror is .......... × 10–10 N.

mV

0.5

2qB 2

Chemistry Section A Q. 31.

92U

C = O is

235

is a member of VI B group. The new element formed by the emission of a-particle will be a member of ....... group : (1) I B (2) II B (3) III B (4) IV B Q. 32. N2 + 3H2 2NH3 1 mole N2 and 3 mole H2 are present at start in 1L flask. At equilibrium NH3 formed required 100mL of 5M HCl for neutralisation hence KC is : (0.5)2 (0.5)2 (1) (2) (0.75) (2.25)3 (0.5)(2.5)3 (3)

Q. 35. The IUPAC name of C2H5 – O

(0.5) L (0.75) (2.5)3



CH3 – CH CH3 (1) ethoxy methanone (2) ethyl-2-methyl propanoate (3) ethoxypropanone (4) 2-methyl ethoxy propanone Q. 36. Which compound would exhibit optical isomers COOH NO2 (1) NO2 COOH

(4) None of these

Q. 33. Which of the following salts undergoes anionic hydrolysis : (1) CuSO4 (2) NH4Cl (3) AlCl3 (4) K2CO3 Q. 34. The dipole moments of the given molecules are such that : (1) BF3 > NF3 > NH3 (2) NF3 > BF3 > NH3 (3) NH3 > NF3 > BF3 (4) NH3 > BF3 > NF3

CH3

(2)

C

OH

H3C COOH HOOC

(3)

C

H

C H COOH

O

(4)

C

304

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 37. When the same amount of zinc is treated separately with excess of sulphuric acid and excess of sodium hydroxide, the ratio of volumes of hydrogen evolved is : (1) 1 : 1 (2) 1 : 2 (3) 2 : 1 (4) 9: 4 Q. 38. On small scale, boron is best isolated by reducing boron trioxide with : (1) Metallic zinc (2) Metallic aluminium (3) Metallic copper (4) Metallic magnesium Q. 39. The pair of compounds which cannot exist together in solution is : (1) NaHCO3 and NaOH (2) NaHCO3 and H2O (3) NaHCO3 and Na2CO3 (4) Na2CO3 and NaOH Q. 40 Which of the following salts will turn water coloured when fumes evolved on treatment with conc. H2SO4 are passed in water : (1) Nitrate (2) Bromide (3) Both (4) None Q. 41. Electrolytic reduction method is used for the extraction of (1) Highly electro negative elements (2) Highly electro positive elements (3) Transition metals (4) Metalloids Q. 42. The number of geometrical isomers of [Co(NH3)3(NO3)3] are : (1) 0 (2) 2 (3) 3 (4) 4 Q. 43. When SO2 is passed through acidified K2Cr2O7 solution : (1) The solution turns blue (2) The solution is decolourised (3) SO2 is reduced (4) Green Cr2(SO4)3 is formed ∆ , CN− → Q. 44. ?  Benzoin. EtOH, H 2 O

The reactant is obtained by dry distillation of the calcium salts of the following pairs : (1) C6H5CH2COOH, HCOOH (2) C6H5COOH, HCOOH (3) C6H4 (OH)COOH, HCOOH (4) C6H4 (NH2)COOH, HCOOH

O

Q. 45.

C C

( A)  → O2

O

O



COOH

H O / soda lime

2  →

Oxidizing agent (A) used is

(1) K2Cr2O7 / H+

(2) AlK . KMnO4

(3) Chromic Acid

(4) V2O5

Q. 46. The presence of primary amines can be confirmed by : (1) Reaction with HNO2 (2) Reaction with CHCl3 and alc. KOH (3) Reaction with Grignard reagent (4) Reaction with Acetyl chloride Q. 47. The monomer of PMMA is : (1) Methyl methacrylate (2) Ethyl acrylate (3) Acrylonitrile (4) Methyl acrylate Q. 48. The activating nature of – CH3 group linked to benzene ring can be explained with the help of (1) Hyperconjugation (2) Resonance effect (3) Inductive effect (4) Electromeric effect Q. 49. In the above reaction if we take methylene chloride and isopropylidene chloride then products are : (1) CH3 – C = CH2 | CH3 (2) CH2=CH2 (3) CH3 – C = C – CH3 | | CH3 CH3 (4) All of the above Q. 50. The compound that will not give iodoform on treatment with alkali and iodine is : (1) Acetone (2) Ethanol (3) Diethyl ketone (4) Isopropyl alcohol

305

Mock Test Paper-14

Section B Q. 51. A compound which contains one atom of X and two atoms of Y for each three atoms of Z is made by mixing 5.00 g of X, 1.15 x 1023 atoms of Y and 0.03 mole of Z atoms. Given that only 4.40   g of compound results. The atomic weight of Y is .......... a.m.u. if the atomic weight of X and Z are 60 and 80 a.m.u. respectively. Q. 52. The minimum uncertainity in velocity of a particle of mass 1.1 × 10–27 kg if uncertainity in its position is 3 × 10–10 cm will be .......... × 10–4 ms–1. Q. 53. A current of 4 amp was passed for 2 hours through a solution of copper sulphate when 5.0 g of copper was deposited. The current efficiency is .......... % (Cu = 63.5). Q. 54. An element A (Atomic weight = 100) having bcc structure has unit cell edge length 400 pm. The number of atoms in 10 g of A is .......... × 1022 unit cells. Q. 55. Phenol associates in benzene to a certain extent to form a dimmer. A solution containing 20 × 10–3 kg phenol in 1 kg of benzene has its freezing point depressed by 0.69 K. The fraction of phenol is .......... mm that has dimerised. Kf for benzene = 5.12 kg mol–1 K.

Q. 56. Two gases A and B having molecular weights 60 and 45 respectively are enclosed in a vessel. The wt. of A is 0.50 g and that of B is 0.2 g. The total pressure of the mixture is 750 mm. The partial pressure of the gases B is .......... mm Hg. Q. 57. 3.5 g of a fuel (with molecular weight 28), was burnt in a calorimeter and raised the temperature of 1 g water from 25° C to 67.3° C. If all the heat generated was used in heating water, the heat of combustion of fuel is – (...........) k cal. Q. 58. The weight of CO is required to form Re2(CO)10 will be .......... g, from 2.50 g of Re2O7 according to given reaction Re2O7 + CO → Re2 (CO)10 + CO2 Atomic weight of Re = 186.2; C = 12 and O = 16. Q. 59. 6.84 g Al2(SO4)3 is needed to coagulate 2.5L of As2S3 sol completely in 2.0 hrs. The coagulation value of Al2(SO4)3 is .......... . Q. 60. 1 mole of an ideal monoatomic gas initially at 1 atm and 300 K experiences a process by which pressure is doubled. The nature of the process is unspecified but DU = 900 cal. The final volume will be .......... l. [Given : R = 0.08 atm lit. / mol/K = 2 Cal / K/ mol J

Mathematics Section A Q. 61. The ratio in which the segment joining the points (2, 4, 5), (3, 5, – 4) is divided by the yz-plane is : (1) – 2 : 3 (2) 2 : 3 (3) 3 : 2 (4) – 3 : 2    Q. 62. For any three vectors a , b and c ,       ( a – b ). ( b – c ) × ( c – a ) =    (1) 0 (2) a . b × c       (3) 2 a . b × c (4) a . c × b Q. 63. If A and B are square matrices of order 3 × 3 and |A| = – 1, |B| = 3, then |3AB| equals : (1) 81 (2) – 81 (3) – 27 (4) – 9

Q. 64. If a, b, c are positive and are the pth, qth and rth terms respectively of a G.P., then the log a p 1 value of log b q 1 is : log c r 1 (1) 0 (2) p (3) q (4) r Q. 65. A coin is tossed twice and the four possible outcomes are assumed to be equally likely. If A is the event, ‘both head and tail have appeared’ and B the event,’ at most one tail is observed,’ then the value of P(B/A) is : (1) 1 (2) 2 (3) 1/2 (4) 1/4

306

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 66. If arg (z) < 0, then arg (– z) – arg (z) = (1) p (2) – p π π (3) – (4) 2 2 sin x Q. 67. The value of dx equals : sin x − cos x 1 1 (1) x + log ( sin x – cos x ) + C 2 2 1 1 (2) x – log ( sin x – cos x ) + C 2 2 (3) x + log (sin x + cos x) + C (4) x – log (sin x + cos x) + C

∫

2

 x , when 0 ≤ x < 1 Q. 68. If f(x) =  , then f ( x ) dx  x , when 1 ≤ x < 2 0 equals : 1 1 (1) (4 2 – 1) (2) ( 4 2 + 1) 3 3 (3) 0 (4) does not exist Q. 69. The area bounded by the x-axis and the curve y = 4x – x2 – 3 is : 1 2 (1) (2) 3 3 4 8 (3) (4) 3 3 Q. 70. The differential equation whose solution is (x – h)2 + (y – k)2 = a2 is (where a is a constant) : 2

∫

3

  dy 2  (1) 1 +    = a2   dx  

 d2 y   2   dx 

2

3

  dy 2  d2 y (2) 1 +    = a2 2 dx   dx   3

  dy   (3) 1 +    = a2   dx  

 d2 y   2   dx 

2

3

d2 y (4)  1 +  dy   = a2 2   dx   dx Q. 71. A particle is moving on a line, where its position S in meters is a function of time t in seconds given by S = t3 + at2 + bt + c where a, b, c are constant. It is known that at t = 1 seconds, the position of the particle is given by S = 7 m. Velocity is 7 m/s and acceleration is 12 m/s2. The values of a, b, c are (1) –3, 2, 7 (2) 3, –2, 5 (3) 3, 2, 1 (4) –3, 2, –1

Q. 72. y = log x satisfies for x > 1, the inequality : (1) x – 1 > y (2) x2 + 1 > y (3) y > x – 1 (4) (x + 1) /x < y Q. 73. The lateral edge of a regular rectangular pyramid is ‘a’ cm long. The lateral edge makes an angle a with the plane of the base. The value of a for which the volume of the pyramid is greatest, is (1)

π 4

(2) sin −1

2 3

π 3 Q. 74. The coordinates of the middle points of the sides of a triangle are (4, 2), (3, 3) and (2, 2) then the coordinates of its centroid are :

(3) cot −1 2

(4)

 7 (1)  3,  (2) (3, 3)  3 (3) (4, 3) (4) (3, 4) Q. 75. The statement p → (q → p) is equivalent to (1) p → (p → q) (2) p → (p ∨ q) (3) p → (p ∧ q)

(4) p → (p ↔ q)

Q. 76. The normal to the ellipse

x2

+

y2

= 1 at a a2 b 2 point P (x1, y1 ) on it, meets the x-axis in G. PN is perpendicular to OX, where O is origin. Then value of  (OG)/ (ON) is : (1) e (2) e2 3 (3) e (4) 1 – e2 Q. 77. The number of points from where a pair of perpendicular tangents can be drawn to the hyperbola, x2 sec2 a – y2 cosec2 a = 1, a ∈ (0, p/4) are : (1) 0 (2) 1 (3) 2 (4) infinite Q. 78. Let x1 = 97, x2 =



x8 =

(1)

2 3 4 , x3 = , x4 = , ……., x1 x2 x3

8 then log 3 x7 3 2

2

   



8

∏ x − 60  = i

i =1



(2) 4

5 2 Q. 79. Let a, b , g, d be the roots of x4 + x2 + 1 = 0. Then the equation whose roots are a2, b2, g2, d2 are :

(3) 6

(4)

307

MOCK TEST PAPER-14 (1) (x4 – x +1) = 0 (2) (x2 + x + 1)2 = 0 (3) (x4 – x2 + 1) = 0 (4) (x2 – x + 1)2 = 0 Q. 80. In usual notation a DABC, if A, A1, A2, A3 be the area of the in-circle and ex-circles, then 1 1 1 + + is equal to A1 A2 A3 (1) (3)

1 A 3 A



(2)



(4)

2 A

A 2

Section B Q. 81. Let ƒ(x) = log x + x3 and let g(x) be the inverse of ƒ(x), then |64g’’(1)| is equal to .......... .  log sin|x| cos x π  | x |< ; x ≠ 0  x 3 Q. 82. If ƒ( x ) =  log sin|3 x| cos , then 2   k x=0 value of k for which ƒ(x) is continuous at x = 0 is .......... . n  1 + ( k − 1)( k + 2)( k + 1)k  π Q. 83. If lim = , cos−1    λ n →∞ k ( k + 1) k =2   then the value of l is .......... . 2

∑

5π  Q. 84. If f(x) = 3 cos  x +  − 5 sin x + 2, 6   maximum value of f(x) is .......... .

then

Q. 85. Range of ‘a’ for which x3 – 12x + [a] = 0 has exactly one real root is (–∞, p) ∪ [q, ∞), then ||p| – |q|| is .......... . Q. 86. If Q(x) is the quotient when P(x) = 1111x1111 – 111x111 + 11x11 – 1011 is divided by x – 1, then sum of the digits in the sum of coefficients of Q(x) is Q. 87. There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, is .......... . Q. 88. If a, b, c, d > 0 such that a + 2b + 3c + 4d = 50, 1/10

 a2 b 4 c3 d  then the maximum value of   16    equal to .......... .

is

Q. 89. The distance between the point P(u, v) and the curve x2 + 4x + y2 = 0 is same as the distance between the points P(u, v) and M(2, 0). If u and v satisfy the relation u2 −

v2 = 1, q

then ‘q’ is .......... . Q. 90. Through the vertex O of parabola y2 = 4x, chords OP and OQ are drawn at right angles to one another, where P and Q are points on the parabola. If the locus of middle point of PQ is y2 = 2(x – l), then value of l is ..........

308

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Answers Physics Q. No.

Answer

1

(2)

2

Topic Name

Q. No.

Answer

Topic Name

Unit & Dimension

16

(4)

Radioactivity

(4)

Vector

17

(2)

X-Ray

3

(1)

One Dimension

18

(1)

Photoelectric Effect

4

(4)

Projectile

19

(4)

Practical Physics

5

(2)

Newton’s Laws of Motion

20

(3)

Communication System

6

(4)

Friction

21

14.00

Work Energy and Power

7

(4)

Calorimetry

22

40.00

Conservation

8

(3)

Kinetic Theory of Gases

23

2.00

Elasticity

9

(2)

Head Conduction

24

2.136

Fluid Mech

10

(2)

Thermal Expansion

25

4.00

Electrostatics

11

(1)

Sound Wave

26

5.00

Capacitance

12

(2)

Refl. at plane surface

27

9.00

Current Electricity

13

(3)

Prism

28

75.00

Magnetic Effect of Current

14

(1)

Wave Optics

29

7.00

Refraction at plane surface

15

(1)

Atomic Structure

30

1.00

Matter Wave

Chemistry Q. No .

Answer

31

(4)

32

Topic Name

Q. No.

Answer

Topic Name

Periodic Table

46

(2)

Nitrogen Containing

(1)

Chemical Equilibrium

47

(1)

Biomolecules

33

(4)

Ionic Equilibrium

48

(1)

General Organic Chemistry

34

(3)

Chemical Bonding

49

(4)

Hydrocarbon

35

(2)

IUPAC

50

(3)

Halogen Derivative

36

(1)

Isomerism

51

70.00

Mole Concept

37

(1)

Hydrogen and Its compound

52

1.50

Atomic Structure

38

(4)

p-Block – Boron

53

52.76

Electrochemistry

39

(1)

s-Block

54

3 .011

Solid State

40

(2)

Salt Analysis

55

746.24

Solution

41

(2)

Metallurgy

56

259.84

Gaseous State

42

(2)

Coordination Compound

57

338.40

Chemical Energetic

43

(4)

Oxygen Family

58

2.456

Redox Reaction

44

(2)

Carbonyl Compound

59

8.00

Surface Chemistry

45

(4)

Carboxylic Acid

60

24.00

Thermodynamics

309

Mock Test Paper-14

Mathematics Q. No.

Answer

61

(1)

62

Topic Name

Q. No.

Answer

Topic Name

Three Dimensional Plane

76

(2)

Ellipse

(1)

Vectors

77

(4)

Hyperbola

63

(2)

Matrices

78

(2)

Logarithms

64

(1)

Determinants

79

(2)

Theory of Equations

65

(1)

Probability

80

(1)

Properties of Triangle

66

(1)

Complex Numbers

81

5.00

Differentiation

67

(1)

Indefinite Integration

82

8.00

Continuity

68

(1)

Definite Integration

83

6.00

Limits

69

(3)

Area Under Curve

84

9.00

Trigonometric Ratios

70

(1)

Differential Equations

85

1.00

Functions

71

(2)

Rate Measure

86

11.0

Binomial Theorem

72

(1)

Monotonicity

87

100

Permutation and Combination

73

(3)

Maxima and Minima

88

5.00

Inequalities

74

(1)

Straight line and Point

89

3.00

Circles

75

(2)

Mathematical Reasoning

90

4.00

Parabola



MOCK TEST PAPER 15 Time : 3 Hours

Total Marks : 300

General Instructions : 1. 2. 3. 4. 5. 6.

There are three subjects in the question paper consisting of Physics (Q. no. 1 to 30), Chemistry (Q. no. 31 to 60) and Mathematics (Q. no. 61 to 90). Each subject is divided into two sections. Section A consists of 20 multiple choice questions & Section B consists of 10 numerical value type questions. In Section B, candidates have to attempt any five questions out of 10. There will be only one correct choice in the given four choices in Section A. For each question 4 marks will be awarded for correct choice, 1 mark will be deducted for incorrect choice for Section A questions and zero mark will be awarded for not attempted question. For Section B questions, 4 marks will be awarded for correct answer and zero for unattempted and incorrect answer. Any textual, printed or written material, mobile phones, calculator etc. is not allowed for the students appearing for the test. All calculations / written work should be done in the rough sheet is provided with Question Paper.

Physics two reflecting surfaces with respect to each other is :

Section A Q. 1. A pebble is thrown vertically upwards from bridge with an initial velocity of 4.9 m/s. It strikes the water after 2 s. If acceleration due to gravity is 9.8 m/s2. The height of the bridge and velocity with which the pebble strike the water will respectively be : (1) 4.9 m, 1.47 m/s (2) 9.8 m, 14.7 m/s (3) 49 m, 1.47 m/s (4) 1.47 m, 4.9 m/s Q. 2. Trajectories of two projectiles are shown in the figure. Let T1 and T2 be the time periods and u1 and u2 be their speeds of projection. Then : Y

1

2 X

(1) T2 > T1 (2) T1 > T2 (3) u1 > u2 (4) u1 < u2 Q. 3. Two blocks each of mass m lie on a smooth table. They are attached to two other masses as shown in the figure. The pulleys and strings are light. An object O is kept at rest on the table. The sides AB and CD of the two blocks are plane and made reflecting. The acceleration of two images formed in those

m

C

A

m

O

B

D

2m

3m

(1)

13 g 6

(2)

11 g 6

17 g 19 g (4) 6 6 Q. 4. Starting from rest, a body slides down a 45° inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is : (1) 0.33 (2) 0.25 (3) 0.75 (4) 0.80 Q. 5. A uniform metal rod of 2 mm2 cross section is heated from 0°C to 20°C. The coefficient of linear expansion of the rod is 12 × 10–6/°C, its Young’s modulus is 1011 N/m2. The energy stored per unit volume of the rod is : (1) 2880 J/m3 (2) 1500 J/m3 3 (3) 5760 J/m (4) 1440 J/m3

(3)

311

MOCK TEST PAPER-15 Q. 6. Calculate the velocity with which the liquid gushes out of the 4 cm2 outlet, if the liquid flowing in the tube is water and liquid in U tube has a specific gravity 12. Velocity of liquid at point A is 20.2 m/s : 2 v = (20.2) m/ s A3 = 6 cm

A 2 cm

B

A1 = 4 cm

2

8 m/s

ρ = 12000 kg/m3

(1) 2.5 m/s (2) 5.5 m/s (3) 8 m/s (4) 10 m/s Q. 7. In a U-tube the radii of two columns are respectively r1 and r2. When a liquid of density r (q = 0°) is filled in it, a level difference of h is observed on two arms, then the surface tension of the liquid is : ρghr1 r2 (1) (2) hrg (r2 – r1) 2( r2 – r1 ) hρg ( r2 – r1 ) 2

(4)

hρg 2( r2 – r1 )

Q. 8. A solid ball of density r1 and radius r falls vertically through a liquid of density r2. Assume that the viscous force acting on the ball is F = krn, where k is a constant and n its velocity. What is the terminal velocity of the ball ? (1) (3)

4 πr 2 (ρ1 – ρ2 ) 3k

(2)

A

(3) P

2 πr(ρ1 – ρ2 ) 3 gk

(2) P

C

A

A2 = 1cm2

2 cm

(3)

(1) P

B

A

C

V

V

(4) P

B

C

B

A C

B V

V

Q. 11. A cylinder of radius R made of material of thermal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 3R made of a material of thermal conductivity K2. The two ends of the combined system are maintained at two different temperature. What is the effective thermal conductivity of the system ? (1) K1 + K2 (3)

K1K 2 K1 + K 2

(2)

K 1 + 8K 2 9

(4)

8K 1 + K 2 9

Q. 12. The speed of a wave in a string is 20 m/s and frequency is 50 Hz. The phase difference between two points on the string 10 cm apart will be : (1) p/2 (2) p (3) 3p/2 (4) 2p Q. 13. If the magnetic lines of force are shaped like arcs of concentric circles with their centre at point O in a certain section of a magnetic field:

2 πg (ρ1 + ρ2 )

(4) None of these 3 gr 2 k Q. 9. The average energy for molecules in one degree of freedom is : 3 kT (1) kT (2) 2 2 3 (3) kT (4) kT 4 Q. 10. A cyclic process ABCA is shown in the V-T diagram. Process on the P-V diagram is : V C

A

B

T

O

(1) The intensity of the field in this section should at each point be inversely proportional to its distance from point O (2) The intensity of the field in this section should at each point be inversely proportional to square of its distance from point O (3) The intensity of the field in this section should at each point be inversely proportional to cube of its distance from point O (4) Nothing can be said

312

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 14. A 6 volt battery is connected to the terminals of a three metre long wire of uniform thickness and resistance of 100 ohm. The difference of potential between two points on the wire separated by a distance of 50 cm will be : (1) 2 volt (2) 3 volt (3) 1 volt (4) 1.5 volt Q. 15. A ray of light from a denser medium strikes a rarer medium at an angle of incidence i as shown in figure. Refracted and reflected rays make an angle of 90° with each other. Angle of reflection and refraction are r and r’. Then critical angle is : N Incident ray Reflected r Denser ray i medium 90º O Rarer Refracted medium r ray

(1)

(1) sin (sin i) (2) sin–1 (sin r) (3) sin–1 (tan i) (4) sin–1 (tan r) Q. 16. In the adjoining figure, AB represents the incident ray and BK the reflected ray. If angle BCF = q, then ∠BFP is given by : B

A P

F

θ

2 fold

(1)

(2) 2 fold

(3) 2 2 fold (4) 4 fold Q. 19. A zener diode is to be used as a voltage regulator. Identify the correct set up : Rs (1) +

RL



–

(2)

+



Rs

RL



–

(3)

+

Rs

RL



K

2  (2) 2  1 +  π 

1 2 2  (3)  1 +  (4)  1 −  2 π π  Q. 18. A camera objective has an aperture diameter d. If the aperture is reduced to diameter d/2, the exposure time under identical conditions of light should be made :

N –1

1 2 1+  2  π

–

(4)

+



Rs

RL

C –

(1) q (2) 2q (3) 3q (4) 2.5q Q. 17. Consider a usual set-up of Young’s double slit experiment with slits of equal intensity as shown in the figure. Take ‘O’ as origin and the Y axis as indicated. If average intensity λD λD between y1 = and y2 = equals n 4d 4d times the intensity of maximum, then n equal is (take average over phase difference): y

S1 d

O S2 D

Q. 20. If the zero of the vernier lies on the right hand side and fourth division coincide with the main scale division when the jaws are in contacts so the correction will be : (1) + 0.04 cm (2) + 0.06 cm (3) –0.04 cm (4) –0.06 cm

Section B Q. 21. A 100 eV electron collides with a stationary helium ion (He+) in its ground state and exits to a higher level. After the collision, + He ions emits two photons in succession with wavelength 1085 Å and 304 Å. The energy of the electron after the collision will be .......... eV. Given h = 6.63 × 10–34 Js.

313

MOCK TEST PAPER-15 Q. 22. The radioactivity of an old sample of whisky due to tritium (half life 12.5 years) was found to be only about 4% of that measured in a recently purchased bottle marked 10 years old. The age of sample is .......... years. Q. 23. The wavelength of Ka line is .......... Pm in copper (Z = 29) if the wavelength of Ka = line in iron (Z = 26) is known to be equal to 193 picometer. Q. 24. A charged dust particle of radius 5 × 10–7 m is located in a horizontal electric field having an intensity of 6.28 × 105 V/m. The surrounding medium is air with coefficient of viscosity h = 1.6 × 10–5 N-s/m2. If the particle moves with a uniform horizontal speed 0.02 m/s, the number of electrons on it is………. . Q. 25. Using a long extension cord in which each conductor has a resistance 8 W, a bulb marked as ‘100 W, 200 V’ is connected to a 220 V dc supply of negligible internal resistance as shown in figure. Power delivered to the bulb is .......... W. I

as shown. The maximum height, ymax is .......... m, at which cart can reach. (g = 10 m/s2) F(N) 50 y max F 1 2 3 4 5

x(m)

x=0

5m

Q. 28. A wedge of mass M = 2 m0 rests on a smooth horizontal plane. A small block of mass m0 rests over it at left end A as shown in figure. A sharp impulse is applied on the block, due to which it starts moving to the right with velocity v0 = 6 m/s. At highest point of its trajectory, the block collides with a particle of same mass m0 moving vertically downwards with velocity v = 2 m/s and gets stuck with it. If the combined mass lands at the end point A of the body of mass M, the length  is .......... cm. Neglect friction, take 2 g = 10 m/s . B

8Ω

20 cm 220V

R = 484Ω 8Ω I

Q. 26. An inductor coil, capacitor and an A.C. source of rms voltage 24 V are connected in series. When the frequency of the source is varied, a maximum rms current of 6.0 A is observed. If this inductor coil is connected to a battery of emf 12 V and of internal resistance 4 W, the current will be .......... Amp. Q. 27. A force shown in the F – x graph is applied to a 5 kg cart, which then coast up a ramp

m0 A  Q. 29. A cubical block of mass 6 kg and side 16.1 cm is placed on frictionless horizontal surface. It is hit by a cue at the top as to impart impulse in horizontal direction. Minimum impulse imparted to topple the block must be greater than .......... kg m/s. Q. 30. The missing number is .......... in the –

at x A

expression given below A = s e where s: displacement, t : time , a : acceleration.

314

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Chemistry Section A Q. 31. Which of the following ions acts as a typical transition metal ion ? (1) Cu+

(2) Sc+

(3) Ti4+

(4) Cr6+

Q. 32. The observed dipole-moment of HCl molecule is 1.03D. If H—Cl bond distance is 1.275 Å and electronic charge is 4.8 × 10–10 esu. What is the percent polarity of HCl : (1) 1.275 Å × 1.03 (2) (3)

4.8 × 10 −10 × 1.275 × 10 −8

Q. 33. For the equilibrium SrCl2 ∙ 6H2O(s)  SrCl2 ∙ 2H2O(s) + 4H2O(g) –12

4

the equilibrium constant KP = 16 × 10 atm at 1°C. If one litre of air saturated with water vapour at 1°C is exposed to a large quantity of SrCl2 ∙ 2H2O(s), what weight of water vapour will be absorbed ? Saturated vapour pressure of water at 1°C = 7.6 torr. (4) 8.5 g

Q. 34. pH of 10–15 M HCl solution is : (1) 7

(2) 6.8

(3) 7.2

(4) 6.5

Q. 35. The correct IUPAC name of the compound is : (1) 5-ethyl-3, 6-dimethyl non -3-ene (2) 5-ethyl-4, 7-dimethyl non-3-ene (3) 4-methyl-5, 7-diethyl oct -2-ene (4) 2,4-ethyl-5-methyl oct-2-ene Q. 36. How many structural isomers possible of the molecular formula C3H6O (excluding enol form)

(1) 5

(2) 7

(3) 8

(4) 9

(3) 2.5 M

(4) 26.8 M

Q. 38. Which one of the following methods is used to prepare borax crystals ? (1) A hot conc. solution of B2O3 is made to react with calculated quantity of conc. H2SO4 (2) Tincal is dried up and heated to red heat

Q. 39. PbCl4 exists but PbBr4 and PbI4 do not because of :

4.8 × 10 −10 (4) × 10 1.03

(3) 2.3 g

(2) 2.68 M

(4)  An alcoholic solution of boric acid is evaporated and cooled.

1.03 × 100 × 10 −18

(2) 6.4 mg

(1) 9.1 M

(3) Tincal is powdered, treated with water and evaporated

4.8 × 10 −10 × 1.275 × 10 −8 1.03

(1) 6 g

Q. 37. A given solution of H2O2 is 30 volumes. Its concentration in terms of molarity is:

(1)  Inability of bromine and iodine to oxidise Pb2+ to Pb4+ (2) Br– and I– are bigger in size (3)  More electropositive character of Br2 and I2 (4) Chlorine is a gas Q. 40. The metallic luster exhibited by sodium is explained by : (1) Diffusion of sodium ions (2) Oscillations of loose electrons (3) Excitation of free protons (4) Existence of body centered cubic lattice. Q. 41. The o, p-directing but deactivating group is (1) – NH2 (2) – OH (3) R-(alkyl) (4) X-(Halogen) Q. 42. When 2-alkyne is treated with sodamide product will be : (1) alkene (2) vinyl acetylene (3) 1-alkyne (4) None of these Q. 43. Benzene on ozonolysis followed by hydrolysis gives : (1) 3 Moles of CH2 = CH2 (2) 3 Moles of C2H2 (3) 3 Moles of CHO – CHO (4) None of these

315

MOCK TEST PAPER-15 Cl 2 / hν [O] → (B) → (C) → Q. 44. (A)  CH3CHO, Identify A, B and C : (1) Ethylalcohol, Ethyl chloride and Ethane (2) Ethane, Ethylchloride and CH3–CH2– OH (3) Propane Propylchloride and CH3 – CH2 – CH2 – OH (4) All of the above aq.KOH

(ii) CO2 /140ºC

Al 2 O3

→ C CH3 COOH

In this reaction, the end product C is : (1) salicylaldehyde (2) salicylic acid (3) phenyl acetate (4) aspirin Q. 46. In the given reaction final product(s) will be: CH3 Na/liq. NH3 (excess)



(A)

O3, Zn H2O

O

(1) CH3–C–CH2–CHO, CH2 O O

(B)

CHO CHO

CHO

(2) CH3–C–C–CH3, CHO O

(3)

(4) (CH2)3

, CH3 C=O CH3 CHO CHO

••

(1) CH2

,

O

Q. 47. Formic acid and formaldehyde can be distinguished by treating with : (1) Benedict’s solution (2) Tollen’s reagent (3) Fehling’s solution (4) NaHCO3 Q. 48. A reaction of ethyl amine and acetic anhydride leads to the formation of : (1) CH3NHCOCH3 (2) C2H5CONHCH3 (3) CH3CONHC2H5 (4) CH3–CH=N–OC2H5 Q. 49. The Non-proteinous substances which certain enzymes require for their activity are called : (1) Catalysts (2) Inhibitors (3) Co-enzymes (4) Epimers

NH2

COO– (2) Bidentate ligand (3) Two donor sites N and O¯ (4) All

Section B

+

(i) NaOH

H / H2O → A  → B Q. 45. Phenol 



Q. 50. Glycinato ligand is :

Q. 51. A gaseous mixture of He and O2 is found to have a density of 0.518 gL–1 at 25° C and 720 torr. The mass percent of helium in this mixture is .......... . –1 Q. 52. The free energy change is – (..........) kJ mol when 1 mole of NaCl is dissolved in water at – 25°C. Lattice energy of NaCl = 777.8 kJ mol 1 –1 ; DS for dissolution = 0.043 kJ mol ; and hydration energy of NaCl = –774.1kJ mol–1. Q. 53. A 10 ml of (NH4)2 SO4 was treated with an excess of NaOH. The evolved NH3 gas absorbed in 50 ml of 0.1 N HCl. 20 ml of 0.1 N NaOH was required to neutralise the remaining HCl. The strength of (NH4)2 SO4 in the solution is .......... g/L. Q. 54. The volume of dilute nitric acid is .......... mL (d = 1.11 g mL–1, 19% w/w HNO3) that can be prepared by diluting with water 50 mL of conc. HNO3 (d = 1.42 g mL–1, 69.8% w/w). Q. 55. When a certain metal was irradiated with light of frequency 3.2 × 1016 Hz, the photoelectrons emitted had twice the kinetic energy as did photoelectrons emitted when the same metal was irradiated with light of frequency 2.0 × 1016 Hz. The light of frequency v0 for the metal is .......... × 1015 Hz. Q. 56. Sea water is found to contain 5.85% NaCl and 9.50% MgCl2 be weight of solution. The normal boiling point of sea water is ..........°C assuming 80% ionisation for NaCl and 50% ionisation of MgCl2 [Kb(H2O) = 0.51 kg mole–1K]. Q. 57. The composition of a sample of wustite is Fe0.93O1.0. The iron is present in the form of Fe(III) is .......... %. Q. 58. The equilibrium constant for the reaction is .......... × 1026. Fe + CuSO4  FeSO4 + Cu at 25°C. Given

E0Fe / Fe2+ = 0.44 V

0 ECu /Cu 2+ = –0.337 V

316

Oswaal JEE (Main) Mock Test 15 Sample Question Papers

Q. 59. The rate of a first order reaction is –1 –1

0.04 mol litre s at 10 minutes and 0.03 mol litre–1 sec–1 at 20 minutes after initiation. The half life of the reaction is .......... min.

Q. 60. A sample of Ferrous sulphide reacts with dil. H2SO4 to from H2S which contains 9% hydrogen by volume. The percentage of fee in the sample, is .......... .

Mathematics Section A Q. 61. If w (≠1) is a cube root of unity and (1 + w)7 = A + Bw, then A and B are respectively the numbers : (1) 0, 1

(2) 1, 1

(3) 1, 0

(4) –1, 1

        Q. 65. The value of [ a +2 b – c ), a – b , a − b − c ] is equal to the box product :       (1) [ a b c ] (2) 2[ a b c ]       (3) 3 [ a b c ] (4) 4 [ a b c ]

Q. 66. The angle between two lines

x +1 y +3 z −4 = = −1 2 2

x −4 y + 4 z +1 x +1 y +3 z −4 and = = is : = = Q. 62. A speaks truth in 75% of the cases and B in 2 1 2 2 −1 2 80% of the cases. The percentage of cases 2 4 they are likely to contradict each other in (1) cos–1   (2) cos–1   9 9 making the same statement is..... 5 7 (1) 25% (2) 35% (3) cos–1   (4) cos–1   9 9 (3) 50% (4) 65% Q. 67. The normal of the curve given by the equation x = a (sin q + cos q), 1+ x x x2 y = a (sin q – cos q) at the point q is : 2 (1) (x + y) cos q + (x – y) sin q = 0 1+ x x Q. 63. If x 2 (2) (x + y) cos q + (x – y) sin q = a x x 1+ x (3) (x + y) cos q – (x – y) sin q = 0 = ax5 + bx4 + cx3 + dx2 + lx + m be an identity (4) (x + y) cos q – (x – y) sin q = a in x, where a, b, c, d, l, m are independent of Q. 68. Function f(x) = x100 + sin x – 1 is increasing x. Then the value of l is for all x ∈ :  π π (1) 3 (2) 2 (1) [0, 1] (2)  − ,   2 2 (3) 4 (4) –3  π  (3)  − , 1 (4) [–π, π]  cos α sin α  Q. 64. If Aa =   2   , then which of  − sin α cos α  Q. 69. The greatest value of the function  1  1 following statement is TRUE ? , 3  is : f(x) = tan–1x – log x in  n n 2  cos α sin α   3  (1) Aa .Ab = Aab & (Aa)n =   n n π 1 π 1  − sin α cos α  (1) + log 3 (2) − log 3 6 4 3 4  cos nα sin nα  n . π 1 π 1 (2) Aa Ab = Aab & (Aa) =   (3) − log 3 (4) + log 3  − sin nα cos nα  6 4 3 4 n n Q. 70. The locus of the mid point of the portion  cos α sin α  (3) Aa.Ab = Aa+b & (Aa)n =   intercept between the axes by the line n n  − sin α cos α  x cos a + y sin a = P where P is a constant is: 1 1 4 2 2 2  cos nα sin nα  (1) x + y = 4P (2) 2 + 2 = (4) Aa.Ab = Aa+b & (Aa)n =   x y P2  − sin nα cos nα  1 1 2 4 (3) x2 + y2 = 2 (4) 2 + 2 = P x y P2

317

MOCK TEST PAPER-15 Q. 71. If 3x + y = 0 is a tangent to the circle with centre at the point (2, –1), then the equation of the other tangent to the circle from the origin is: (1) x – 3y = 0 (3) 3x – y = 0

(2) x + 3y = 0 (4) 2x + y = 0

Q. 72. The equation of the line touching both the parabolas y2 = x and x2 = y is (1) 4x + 4y + 1 = 0 (2) 4x + 4y – 1 = 0 (3) x + y + 1 = 0

(4) 4x – 4y + 1 = 0

Q. 79. If a, b, g, d are roots of 1 1 x4 – 100x3 + 2x2 + 4x + 10 = 0, then + β α 1 1 + + is equal to γ δ 2 1 (1) (2) 5 10 2 (3) 4 (4) – 5 Q. 80. If 0 < x, y, a, b < 1, then the sum of the infinite terms of the series x ( a + x ) +

(1) A Tautology

… is :

(2) A contradiction (3) A tautology and a contradiction (4) neighter tautology nor a contradiction π Q. 74. If sin q = and < q < p. Then the 2 2 sin θ + cos θ value of is : tan θ (1) 0 (2) 1 1 (3) (4) 2 2 Q. 75. The general solution of x satisfying 3 π x cot  −  = is..... 3 4 3

1

π (12n – 1) ; n ∈ I 2 π (2) (12n + 1) ; n ∈ I 2 −π (3) (12n + 1) ; n ∈ I 12 π (4) (12n + 1); n ∈ I 12

(1)

Q. 76. cos–1 (cos 10) is equal to (1) 4p + 10

(2) 4p – 10

(3) – 4p + 10

(4) 10

Q. 77. Let ABC be a triangle such that ∠A = 45°, ∠B = 75° then a + c 2 is equal to : (in usual notation) (1) 0

(2) b

(3) 2b

(4) –b

Q. 78. If H is the orthocentre of the triangle ABC, then AH is equal to : (1) a cot A

(2) a cot B

(3) b cot A

(4) c cot A

(1) (3)

xy ) +

x ( ab +

Q. 73. (p ⇒ q) ∩ (q ⇒ r) ⇒ (p ⇒ r) is.....

ax 1+ b x 1− b

+ +

x 1+ y x 1− y

(2) (4)

x (b a + y x ) +

x 1+ b ax 1− b

+ +

Section B

x 1+ y x 1− y

n

 1  Q. 81. In the binomial expansion of  3 2 + 3  , 3  the ratio of the 7th term from the beginning to the 7th term from the end is 1 : 6 ; n is ...... . Q. 82. The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be .......... .

Q. 83. The point on the ellipse x2 + 2y2 = 6 closest to the line x + y = 7 is (a, b). The value of (a + b) will be .......... . Q. 84. The hyperbola

x2

−

y2

= 1 passes through a2 b 2 the point of intersection of the lines, 7x + 13y – 87 = 0 and 5x – 8y + 7 = 0, the 2 latus rectum is 32 . The value of a 2 + b 5 will be .......... .

(

)

Q. 85. Let ƒ(x) be a function which satisfies ƒ(x3)ƒ’(x) = ƒ’(x)ƒ’(x3) + ƒ’’(x2). Given that ƒ(1) = 1 and ƒ’’’(1) = 1/4, then value of 4(ƒ’(1) + ƒ’’(1)) is .......... .

318

Oswaal JEE (Main) Mock Test 15 Sample Question Papers (18 x a + 15x b - 10 x g )d , then (3a + 4b + 5g q + 6d + 7q) is .......... . (Where d is a rational

2 2 2 4 4 4 Q. 86. lim (1 + 2 + ...... + n )(1 + 2 + ...... + n ) = k + 1  , 7 7 7

(1 + 2 + ......n )

n ®¥



15

then k is equal to .......... .

Q. 87. Let ƒ : R → R and ƒ be a differentiable function such that ƒ(x + 2y) = ƒ(x) + 4ƒ(y) + 2y(2x – 1) " x, y ∈ R and ƒ’(0) = 1, then ƒ(3) + ƒ’(3) is equal to .......... . 1 1 2 2 Q. 88. If x + y = t + and x + y = t 2 + 2 then t t dy 150 x 2 is .......... . dx

number in its simplest form) 1 n

ò tan

Q. 90.

1 If lim n +11 n ®¥ n

-1

( nx ) dx =

ò sin

-1

p , (where p and q q

( nx ) dx

1 n +1

Q. 89. If ƒ(x)= ò (3x - 1)x( x + 1)(18 x11 + 15x10 - 10 x 9 )1/ 6 dx , where ƒ(0) = 0, is in the form of

are coprime), then (p + q) is .......... .

Answers Physics Q. No.

Answer

1

(2)

2

(4)

3

Topic Name

Q. No.

Answer

Topic Name

One Dimension

16

(2)

Reflection at Curve Surface

Projectile

17

(1)

Wave Optics

(3)

Newton’s Law of Motion

18

(4)

Optical Instruments

4

(3)

Friction

19

(1)

Solid & Semi-Conductor

5

(1)

Elasticity

20

(3)

Practical Physics

6

(2)

Fluid

21

47.70

Atomic Structure

7

(1)

Surface Tension

22

68.00

Radioactivity

8

(1)

Viscocity

23

154

X-Ray

9

(2)

Kinetic Theory of Gases

24

30.00

Electrostatics

10

(3)

Thermodynamics

25

93.70

Current Electricity

11

(2)

Heat Conduction

26

1.50

Alternating Current

12

(1)

Transverse Wave

27

2.00

Work Energy and Power

13

(1)

Magnetism

28

40.00

Conservation Law

14

(3)

Electrical Instruments

29

4.00

Rotational Motion

15

(4)

Reflection at Plane Surface

30

2.00

Unit & Dimension

Chemistry Q. No.

Answer

31

(2)

32

Topic Name

Q. No.

Answer

Topic Name

Periodic Table

46

(1)

Hydrocarbons

(3)

Chemical Bonding

47

(4)

Carboxylic Acid

33

(2)

Chemical Equilibrium

48

(3)

Nitrogen Compound

34

(1)

Ionic Equilibrium

49

(3)

Biomolecules

35

(1)

General Organic Chemistry

50

(4)

Coordination Compound

36

(2)

Isomerism

51

19.90

Gaseous State

37

(2)

Hydrogen Family

52

9.114

Thermodynamics

319

Mock Test Paper-15 38

(3)

p-Block-Boran

53

19.80

Redox Reaction

39

(1)

p-Block-Carbon

54

234.98

Mole Concept

40

(2)

s-Block

55

8.00

41

(4)

General Organic Chemistry

56

101.99

Solution

42

(3)

Hydrocarbon

57

15.05

Solid State

43

(3)

Aromatic Compound

58

1.71

Electrochemistry

44

(2)

Halogen Derivatives

59

24.00

Chemical Kinetics

45

(4)

Alcohol, Ether and Phenol

60

5.92

Salt Anaylsis

Atomic Structure

Mathematics Q. No.

Answer

61

(2)

62

Topic Name

Q. No.

Answer

Topic Name

Complex Number

76

(2)

Inverse trigonometric Functions

(2)

Probability

77

(3)

Solution of Triangles

63

(1)

Determinant

78

(1)

Radii of Circle

64

(4)

Matrices

79

(4)

Quadratic Equation

65

(3)

Vector

80

(4)

Progression

66

(2)

Three Dimensional Plane

81

9.00

Binomial Theorem

67

(3)

Tangent and Normal

82

18720

68

(1)

Monotonicity

83

3.00

Ellipse

69

(1)

Maxima and Minima

84

9.00

Hyperbola

70

(2)

Straight Line

85

3.00

Function

71

(1)

Circle

86

7.00

Limit

72

(1)

Parabola

87

19.00

Continuity & Differetiability

73

(1)

Mathematical Reasoning

88

150.00

Differentiation

74

(1)

Trigonometric Ratio

89

298

Indefinite Integration

75

(3)

Trigonometric Equation

90

3.00

Definite Integration

Permutation and Combination

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