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Chapterwise Topicwise Solved Papers 2021-1979 IITJEE JEE Main & Advanced Physics DC Pandey Arihant Prakashan (Series), Meerut Arihant Prakashan (Series), Meerut All Rights Reserved © Author Administrative & Production Offices Regd Office ‘Ramchhaya’ 4577/15, Agarwal Road, Darya Ganj, New Delhi -110002 Tele: 011- 47630600, 43518550 Head Office Kalindi, TP Nagar, Meerut (UP) - 250002, Tel: 0121-7156203, 7156204 Sales & Support Offices Agra, Ahmedabad, Bengaluru, Bareilly, Chennai, Delhi, Guwahati, Hyderabad, Jaipur, Jhansi, Kolkata, Lucknow, Nagpur & Pune ISBN 978-93-25796-15-7 PO No : TXT-XX-XXXXXXX-X-XX Published by Arihant Publications (India) Ltd For further information about the books published by Arihant, log on to www.arihantbooks.com or e-mail at info@arihantbooks.com Follow us on Preface Dear students it gives me immense pleasure to present this book in a new format I have been a part of the education sector for more than 25 years I have observed that IIT-JEE problems are really good and conceptual (except 1%) Most of our teaching fraternity have developed our concepts from these problems But there has always existed a confusion amongst the students, about "how to segregate the problems which need to be practiced before and after JEE Mains?" I was also with this question many times but could not spare time to segregate them But now I used this lockdown period as an opportunity to upgrade my book and now it's more student friendly To extract best out of my book, it is divided into following three parts l Section problems be attempted before JEE Mains l Section problems be attempted after JEE Mains and l Section problems consisting of above mentioned 1% problems Students can skip this section I have tried my level best to keep errors out of this book A special note of thanks is due to Mr Anoop Dhyani for their special contribution I shall be highly grateful to the readers who point out any errors in my mail id : arihantcorrections@gmail.com Thanks and Regards DC Pandey Dedication This book is dedicated to my honourable grandfather (Late) Sh Pitamber Pandey (a Kumaoni poet; resident of village Dhaura (Almora) Uttarakhand) CONTENTS General Physics 1-20 Kinematics 21-36 Laws of Motion 37-55 Work, Power and Energy 56-70 Centre of Mass 71-94 Rotation Gravitation 134-147 Simple Harmonic Motion 148-166 Properties of Matter 167-193 10 Wave Motion 194-223 11 Heat and Thermodynamics 224-282 12 Optics 283-346 13 Current Electricity 347-378 14 Electrostatics 379-438 15 Magnetics 439-483 16 Electromagnetic Induction and Alternating Current 484-517 17 Modern Physics 518-584 JEE Advanced Solved Paper 2020 JEE Advanced Solved Paper 2021 585-598 1-16 95-133 SYLLABUS JEE MAIN SECTION A (80% weightage) UNIT I Physics and Measurement Physics, technology and society, SI units, Fundamental and derived units Least count, accuracy and precision of measuring instruments, Errors in measurement, Significant figures Dimensions of Physical quantities, dimensional analysis and its applications UNIT II Kinematics Frame of reference Motion in a straight line: Positiontime graph, speed and velocity Uniform and nonuniform 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 III Laws of Motion 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 Static and Kinetic friction, laws of friction, rolling friction Potential energy of a spring, conservation of mechanical energy, conservative and nonconservative forces; Elastic and inelastic collisions in one and two dimensions UNIT V Rotational Motion Centre of mass of a two-particle system, Centre of mass of a rigid body; Basic concepts of rotational 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 body rotation, equations of rotational motion UNIT VI Gravitation The universal law of gravitation Acceleration due to gravity and its variation with altitude and depth Kepler's laws of planetary motion Gravitational potential energy; gravitational potential Escape velocity Orbital velocity of a satellite Geo-stationary satellites UNIT VII Properties of Solids & Liquids Dynamics of uniform circular motion: Centripetal force and its applications Elastic behaviour, Stress-strain relationship, Hooke's Law, Young's modulus, bulk modulus, modulus of rigidity UNIT IV Work, Energy and Power Pressure due to a fluid column; Pascal's law and its applications Work done by a constant force and a variable force; kinetic and potential energies, work-energy theorem, power Viscosity, Stokes' law, terminal velocity, streamline and turbulent flow, 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 Electric field Electric field due to a point charge, Electric field lines, Electric dipole, Electric field due to a dipole, Torque on a dipole in a uniform electric field Heat, temperature, thermal expansion; specific heat capacity, calorimetry; change of state, latent heat Electric flux, Gauss's law and its applications to find field due to infinitely long, uniformly charged straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell Heat transfer-conduction, convection and radiation, Newton's law of cooling UNIT VIII Thermodynamics Thermal equilibrium, zeroth law of thermo-dynamics, concept of temperature Heat, work and internal energy First law of thermodynamics Second law of thermodynamics: reversible and irreversible processes Camot engine and its efficiency UNIT IX Kinetic Theory of Gases 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 with and without dielectric medium between the plates, Energy stored in a capacitor Equation of state of a perfect gas, work done on compressing a gas UNIT XII Current Electricity Kinetic theory of gases - assumptions, concept of pressure Kinetic energy and temperature: rms speed of gas molecules; Degrees of freedom, Law of equipartition of energy, applications to specific heat capacities of gases; Mean free path, Avogadro's number 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 UNIT X Oscillations and Waves Electric Cell and its Internal resistance, potential difference and emf of a cell, combination of cells in series and in parallel Periodic motion - period, frequency, displacement as a function of time Periodic functions Simple harmonic motion (S.H.M.) and its equation; phase; oscillations of a spring - restoring force and force constant; energy in S.H.M - kinetic and potential energies; Simple pendulum - derivation 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 UNIT XI Electrostatics Electric charges Conservation of charge, Coulomb's law-forces between two point charges, forces between multiple charges; superposition principle and continuous charge distribution Kirchhoff's laws and their applications Wheatstone bridge, Metre bridge Potentiometer - principle and its applications UNIT XIII Magnetic Effects of Current and Magnetism Biot-Savart law and its application to current 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 currentcarrying conductors-definition of ampere Torque experienced by a current loop in uniform magnetic field, Moving coil galvanometer, its current sensitivity and conversion to ammeter and voltmeter Current loop as a magnetic dipole and its magnetic dipole moment Bar magnet as an equivalent solenoid, magnetic field lines; Earth's magnetic field and magnetic elements Para, dia and ferro-magnetic substances Magnetic susceptibility and permeability, Hysteresis, Electromagnets and permanent magnets Polarisation, plane polarized light; Brewster's law, uses of plane polarized light and Polaroids UNIT XVII Dual Nature of Matter and Radiation Dual nature of radiation Photoelectric effect, Hertz and Lenard's observations; Einstein's photoelectric equation; particle nature of light UNIT XIV Electromagnetic Induction and Alternating Currents Matter waves-wave nature of particle, de Broglie relation Davisson-Germer experiment Electromagnetic induction; Faraday's law, induced emf and current; Lenz's Law, Eddy currents Self and mutual inductance UNIT XVIII Atoms and Nuclei 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 UNIT XV Electromagnetic Waves Electromagnetic waves and their characteristics Transverse nature of electromagnetic waves Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) Applications of e.m waves UNIT XVI Optics Reflection and refraction of light at plane and spherical surfaces, mirror formula, Total internal reflection and its applications, Deviation and Dispersion of light by a prism, Lens Formula, Magnification, Power of a Lens, Combination of thin lenses in contact, Microscope and Astronomical Telescope (reflecting and refracting) and their magnifying powers Wave optics wave front and Huygens' principle, Laws of reflection and refraction using Huygen's principle Interference, Young's double slit experiment and expression for fringe width, coherent sources and sustained interference of light Diffraction due to a single slit, width of central maximum Resolving power of microscopes and astronomical telescopes, 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; binding energy per nucleon and its variation with mass number, nuclear fission and fusion UNIT XIX Electronic Devices Semiconductors; semiconductor diode: I-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 configuration) and oscillator Logic gates (OR, AND, NOT, NAND & NOR) Transistor as a switch UNIT XX Communication Systems Propagation of electromagnetic waves in the atmosphere; Sky and space wave propagation, Need for modulation, Amplitude and Frequency Modulation, Bandwidth of signals, Bandwidth of Transmission medium, Basic Elements of a Communication System (Block Diagram only) SECTION B (20% weightage) UNIT XXI Experimental Skills Familiarity with the basic approach and observations of the experiments and activities Vernier callipers - its use to measure internal and external diameter and depth of a vessel Screw gauge - its use to determine thickness/ diameter of thin sheet/wire Simple Pendulum - dissipation of energy by plotting a graph between square of amplitude and time Metre Scale - mass of a given object by principle of moments Young's modulus of elasticity of the material of a metallic wire Surface tension of water by capillary rise and effect of detergents Coefficient of Viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body Plotting a cooling curve for the relationship between the temperature of a hot body and time Speed of sound in air at room temperature 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 (i) Comparison of emf of two primary cells (ii) Determination of Internal resistance of a cell 14 Resistance and figure of merit of a galvanometer by half deflection method 15 Focal length of (i) Convex mirror (ii) Concave mirror (iii) Convex lens Using parallax method 16 Plot of angle of deviation vs angle of incidence for a triangular prism 17 Refractive index of a glass slab using a travelling microscope 18 Characteristic curves of a p-n junction diode in forward and reverse bias 19 Characteristic curves of a Zener diode and finding reverse break down voltage 20 Characteristic curves of a transistor and finding current gain and voltage gain 21 Identification of Diode, LED, Transistor, IC, Resistor, Capacitor from mixed collection of such items 22 Using multimeter to (i) Identify base of a transistor (ii) Distinguish between npn and pnp type transistor (iii) See the unidirectional flow of current in case of a diode and an LED (iv) Check the correctness or otherwise of a given electronic component (diode, transistor or IC) JEE ADVANCED General Units and dimensions, dimensional analysis, least count, significant figures, Methods of measurement and error analysis for physical quantities pertaining to the following experiments, Experiments based on using vernier calipers and screw gauge (micrometer), Determination of g using simple pendulum, Young's modulus by Searle's method, Specific heat of a liquid using calorimeter, focal length of a concave mirror and a convex lens using u-v method, Speed of sound using resonance column, Verification of Ohm's law using voltmeter and ammeter, and specific resistance of the material of a wire using meter bridge and post office box Mechanics Kinematics in one and two dimensions (Cartesian coordinates only), projectiles, Circular motion (uniform and non-uniform), Relative velocity Newton's Laws of Motion, Inertial and uniformly accelerated frames of reference, Static and dynamic friction, Kinetic and potential energy, Work and power, Conservation of linear momentum and mechanical energy Systems of Particles, Centre of mass and its motion, Impulse, Elastic and inelastic collisions Law of Gravitation, Gravitational potential and field, Acceleration due to gravity, Motion of planets and satellites in circular orbits, Escape velocity Rigid body, moment of inertia, parallel and perpendicular axes theorems, moment of inertia of uniform bodies with simple geometrical shapes, Angular momentum, Torque, Conservation of angular momentum, Dynamics of rigid bodies with fixed axis of rotation, Rolling without slipping of rings, cylinders and spheres, Equilibrium of rigid bodies, Collision of point masses with rigid bodies Linear and angular simple harmonic motions Hooke's law, Young's modulus Pressure in a fluid, Pascal's law, Buoyancy, Surface energy and surface tension, capillary rise, Viscosity (Poiseuille's equation excluded), Stoke's law, Terminal velocity, Streamline flow, Equation of continuity, Bernoulli's theorem and its applications Wave motion (plane waves only), longitudinal and transverse waves, Superposition of waves; progressive and stationary waves, Vibration of strings and air columns Resonance, Beats, Speed of sound in gases, Doppler effect (in sound) Centre of Mass 38 An α-particle of mass m suffers one-dimensional elastic collision with a nucleus at rest of unknown mass It is scattered directly backwards losing 64% of its initial kinetic energy The mass of the nucleus is (2019 Main) (a) 1.5 m (b) m (c) 3.5 m (d) m 75 platform and the spring’s maximum compression is found to be x Given that g = 10 ms −2 , the value of x will be close to (2019 Main) (a) cm (b) cm (c) 40 cm (d) 80 cm Objective Question II (One or more correct option) 39 A satellite of mass M is in a circular orbit of radius R about 44 Two blocks A and B each of mass m, are connected by a the centre of the earth A meteorite of the same mass falling towards the earth collides with the satellite completely inelastically The speeds of the satellite and the meteorite are the same just before the collision The subsequent motion of the combined body will be (2019 Main) (a) in the same circular orbit of radius R (b) in an elliptical orbit (c) such that it escapes to infinity (d) in a circular orbit of a different radius massless spring of natural length L and spring constant k The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A and B, and collides elastically with A Then (1993) v L C A B 40 A simple pendulum is made of a string of length l and a bob of mass m, is released from a small angle θ It strikes a block of mass M , kept on a horizontal surface at its lowest point of oscillations, elastically It bounces back and goes up to an (2019 Main) angle θ1 Then, M is given by θ + θ1 m θ − θ1 (a) m (b) θ + θ1 θ − θ1 (a) the kinetic energy of the A-B system, at maximum compression of the spring, is zero (b) the kinetic energy of the A-B system, at maximum compression of the spring, is mv2 / θ − θ1 (c) m θ + θ1 (d) the maximum compression of the spring is v (d) m θ + θ1 θ − θ1 41 A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building At the same time, a bullet of mass 0.02 kg is fired vertically upward with a velocity 100 ms −1 from the ground The bullet gets embedded in the wood Then, the maximum height to which the combined system reaches above the top of the building before falling below is (Take, g = 10 ms −2 ) (2019 Main) (a) 20 m (b) 30 m (c) 10 m (d) 40 m 42 Three blocks A , B and C are lying on a smooth horizontal surface as shown in the figure A and B have equal masses m while C has mass M Block A is given an initial speed v towards B due to which it collides with B perfectly inelastically The combined mass collides with C, also perfectly inelastically th of the initial kinetic energy is lost M in whole process What is value of ? m (2019 Main) (a) (c) A B C m m M (b) (d) *43 A body of mass kg falls freely from a height of 100 m on a platform of mass kg which is mounted on a spring having spring constant k = 125 × 106 N/m The body sticks to the (c) the maximum compression of the spring is v ( m/ k ) ^ m 2k ^ 45 Two balls, having linear momenta p1 = p i and p2 = − p i , undergo a collision in free space There is no external force acting on the balls Let p′1 and p′ be their final momenta The following option is (are) not allowed for any non-zero value of p , a1 , a2 , b1 , b2 , c1 and c2 (2008) $ $ $ $ $ (a) p′ = a i + b j + c k , p′ = a i + b j 1 1 2 (b) p1′ = c1 k$ , p′2 = c2 k$ (c) p′1 = a1 $i + b1 $j + c1 k$ , p′2 = a2 i$ + b2 $j − c1 k$ (d) p′ = a $i + b $j , p′ = a i$ + b $j 1 2 46 A point mass of kg collides elastically with a stationary point mass of kg After their collision, the kg mass reverses its direction and moves with a speed of ms −1 Which of the following statement(s) is/are correct for the system of these two masses? (2010) (a) Total momentum of the system is kg-ms −1 (b) Momentum of kg mass after collision is kg -ms −1 (c) Kinetic energy of the centre of mass is 0.75 J (d) Total kinetic energy of the system is J Passage Based Questions Passage A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure The angle of the incline suddenly changes from 60° to 30° at point B The block is 76 Centre of Mass initially at rest at A Assume that collisions between the block and the incline are totally inelastic(g = 10 m/s2) A M decreases and then increases Does this violate the conservation of momentum principle? (1979) 54 A circular plate of uniform thickness has a diameter of v 60° 53 When a ball is thrown up, the magnitude of its momentum 56 cm A circular portion of diameter 42 cm is removed from one edge of the plate as shown in figure Find the position of the centre of mass of the remaining portion (1980) B 30° C 3Ö3 m Ö3 m 47 The speed of the block at point B immediately after it strikes the second incline is (a) 60 m/s (b) 45 m/s (2008) (c) 30 m/s (d) 15 m/s 42 cm 56 cm 48 The speed of the block at point C, immediately before it leaves the second incline is (a) 120 m/s (b) 105 m/s (c) 90 m/s (2008) (d) 75 m/s 49 If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is (2008) (a) 30 m/s (b) 15 m/s (c) zero (d) − 15 m/s Integer Answer Type Questions 50 Three objects A , B and C are kept in a straight line on a frictionless horizontal surface These have masses m, 2m and m, respectively The object A moves towards B with a speed ms −1 and makes an elastic collision with it Thereafter, B makes completely inelastic collision with C All motions occur on the same straight line Find the final speed (in ms −1 ) of the object C (2009) m 2m m A B C 51 A solid horizontal surface is covered with a thin layer of oil A rectangular block of mass m = 0.4 kg is at rest on this surface An impulse of 1.0 N s is applied to the block at time t = 0, so that it starts moving along the X -axis with a velocity v ( t ) = v0 e− t / τ , where v0 is a constant and τ = s The displacement of the block, in metres, at t = τ is (Take, e−1 = 0.37) (2018 Adv.) Analytical & Descriptive Questions 52 A body of mass m moving with a velocity v in the x-direction collides with another body of mass M moving in the y-direction with a velocity V They coalesce into one body during collision Find (a) the direction and magnitude of the momentum of the composite body (b) the fraction of the initial kinetic energy transformed into heat during the collision (1978) 55 A body of mass kg initially at rest, explodes and breaks into three fragments of masses in the ratio : : The two pieces of equal mass fly-off perpendicular to each other with a speed of 30 m/s each What is the velocity of the heavier fragment ? (1981) 56 Three particles A , B and C of A equal mass move with equal speed v along the medians of an equilateral triangle as shown in figure They collide at the centroid G of the triangle After the collision, A comes to rest, B retraces its path with the speed v What is the velocity of C? G C B (1982) 57 A small sphere of radius R is held against the inner surface of a larger sphere of radius 6R The masses of large and small spheres are 4M and M respectively This arrangement is placed on a horizontal table There is no friction between any surfaces of contact The small sphere is now released Find the coordinates of the centre of the larger sphere when the smaller sphere reaches the other extreme position (1996) Y 6R M, R X 4M (L, 0) 58 A particle of mass m, moving in a Y v1 v2 circular path of radius R with a constant speed v2 is located at R point ( 2R , ) at time t = and a (0,0) X man starts moving with a velocity m v1 along the positive Y-axis from origin at time t = Calculate the linear momentum of the particle w.r.t man as a function of time (2003) SECTION - Objective Questions I (Only one correct option) This question has statement I and statement II Of the four choices given after the statements, choose the one that best describes the two statements (2013 Main) Statement I A point particle of mass m moving with speed v collides with stationary point particle of mass M If the 1 maximum energy loss possible is given as f mv2 , then 2 m f = M + m Statement II Maximum energy loss occurs when the particles get stuck together as a result of the collision (a) Statement I is true, Statement II is true, and Statement II is the correct explanation of Statement I (b) Statement I is true, Statement II is true, but Statement II is not the correct explanation of Statement I (c) Statement I is true, Statement II is false (d) Statement I is false, Statement II is true A person of mass M is sitting on a swing to length L and swinging with an angular amplitude θ If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance l ( l