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Physics IIT JEE Engineering Solved Papers 2005-2019 chapter wise topic wise problems questions solutions fully solved PDF

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CHAPTERWISE TOPICWISE ENGINEERING ENTRANCES SOLVED PAPERS 2019 -2005 PHYSICS A Master Collection ofE xams Questions to Practice for JEE MAIN & ADVANCED 2020 Author Vikas Jain *arihant ARIHANT PRAKASHAN (Series), MEERUT ,:carihant ARIHANT PRAKASHAN (SERIES), MEERUT All Rights Reserved !fi © Publisher No part of this publication may be re-produced, stored in a retrieval system or by any means, electronic, mechanical, photocopying, recording, scanning, web or otherwise without the written permission of the publisher. Arihant has obtained all the information in this book from the sources believed to be reliable and true. However, Arihant or its editors or authors or illustrators don't take anyresponsibilityfor the absolute accuracy of any information published and the damage or loss suffered thereupon. All disputes subject to Meerut (UP) jurisdiction only. !fi 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 !fi Sales & Support Offices Agra, Ahmedabad, Bengaluru, Bareilly, Chennai, Delhi, Guwahati, Hyderabad, Jaipur, J hansi, Kolkata, Lucknow, Nagpur & Pune. !fi ISBN 978-93-13199-66-3 Published by Arihant Publications (India) Ltd. For further information about the books published by Arihant, log on to www.arihantbooks.com ore-mail at [email protected] a Followuson O ~ @) PREFACE Once you have an idea of what you are going to be asked in a test, you are more comfortable to tackle it, and your performance in the test improves dramatically. Once you know the importance of different chapters and topics from the syllabi for a exam by going through chapterwise and topical segregation of previous years' questions, you can strategically plan out your preparation for the exam by allotting your time accordingly for the chapters or the topics of the chapters. This book Chapterwise & Topicwise Engineering Entrances Solved Papers Physics has Previous Years' Engineering Entrance Questions with their Solutions to fulfill the above mentioned needs of understanding the nature & pattern of questions being asked in JEE Main & Advanced and other Engineering Entrances. The Salient Features oft he Book a re • It covers all the questions with explanations from year 2005 to 2019 for all engineering entrance exams in India (both National as well as RegionaO. • Chapterwise division and topical categorisation has been done keeping in mind the syllabi of various engineering entrance exams and NCERTTextbooks • Questions of all engineering entrances are grouped according to the year. • Extreme care is taken, while solving the questions and compiling their explanations for their accuracy. We hope that the book will be of utmost help to you in your studies, and propel you to success in the engineering entrance exams. Suggestions for further improvement are welcome. Publisher CONTENTS th [ PART 1] Based on Class Xl NCERT 1. Units and Measurements 1-22 7. Systems of Particles and Units Rotational Motion 148-183 Dimensions Centre of Mass Error in Measurement Angular Displacement, Velocity and Acceleration 2. Motion in a Straight Line 23-51 Moment of Inertia Distance and Displacement Torque, Couple and Angular Momentum Uniform and Non-uniform Motion Rotational Energy and Power Graphs Rolling Motion 3. Motion in a Plane I (Vectors) 52-65 8. Gravitation 184-206 Fundamental of Vectors Newton's Law of Gravitation Addition and Substraction of Vectors Acceleration due to Gravity Multiplication ofV ectors Gravitational Potential, Energy and Relative Motion Escape Velocity Motion of Satellites and Kepler's Laws of 4. Motion in a Plane (Two and Three Planetary Motion Dimensions) 66-86 Uniform and Non-uniform Circular Motion 9. Mechanical Properties of Solids 207-218 Projectile Motion Hooke's Law: Young's Bulk and Rigidity Modulus s. Laws of Motion 87-119 Work Done in Stretching a Wire Newton's Laws of Motion Poisson's Ratio and Thermal Stress Conservation of Linear Momentum Equilibrium of Forces 10. Mechanical Properties of Fluids 219-245 Motion of Connected Bodies and Friction Pressure and Density Motion on Inclined Surfaces Pascal's Law and Archimedes' Principle Fluid Law 6. Work, Energy and Power 120-147 Surface Tension and Surface Energy Work Done Pressure Difference Energy Angle of Contact and Capillarity Power Collisions 11. Thermal Properties of Matter 246-273 Degree of Freedom and Specific Heat Thermometry (Mean Free Path) Thermal Expansion 14. Oscillations 311-338 Calorimetry Displacement of SHM and Phase Thermal Conduction Velocity, Acceleration and Energy SHM Radiation (General, Kirchhoff's Law and Time Period and Frequency Black Body) Simple Pendulum and its Applications Radiation (Wien's Law,Stefan's Law and Superposition ofSHM and Resonance Newton's Law of Cooling) 15. Waves 339-376 12. Thermodynamics 274-296 Basics of Mechanical Waves First Law of Thermodynamics Progressive Waves Thermodynamic Process Interference and superposition Waves Heat Engine, Refrigerator and Second Law of Thermodynamics Beats Stationary Waves: Vibrations of Strings and 13. Kinetic Theory of Gases 297-310 Organ Pipes Gas Laws Doppler's Effect Various Speed of Gases Musical Sounds and Acoustics of Buildings Pressure and Energy of Gas I PART 11] Based on Class XI Ith NCERT 16. Electrostatics I 377-422 19. Current and Electricity II 497-511 Electric Charge and Coulomb's Law Heating Effects of Current Electric Field Thermoelectricity Electric Dipole Chemical Effects of Current Electric Potential and Potential Energy 20. Moving Charges and Magnetism 512-544 Electric Flux and Gauss'Theorem Biot-Savart's Law and Ampere's Circuital Law 17. Electrostatics II (Capacitance) 423-446 Motion of a Charged Particle in a Capacitance and Capacitors Magnetic Field Grouping of Capacitor Force and Torque on a Current Carrying Conductor 18. Current Electricity 447-496 Electric Conduction, Ohm's Law and Resistance 21. Magnetism and Matter 545-561 Magnet and their Properties Combination of Resistances Earth's Magnetism Kirchhoff's Law Cells and their Combination Magnetic Equipments Different Measuring Instruments Magnetic Material 22. Electromagnetic Induction 562-579 Diffraction of Light Faraday's Law, Lenz's Law and Motional EMI Polarisation of Light Motional and Static EMI 27. Dual Nature of Radiation & Matter 680-707 Applications of EMI (Motor, Dynamo, Cathode Rays & Positive Rays Transformer) Dual Nature of Matter: de-Broglie Waves 23. Alternating Current 580-002 Photon & Photoelectric Effect Alternating Current, Voltage and Power X-Rays AC Circuits 28. Atoms and Nuclei 708-750 Growth and Decay of Currents Early Atomic Structure 24. Electromagnetic Waves 603-ol 1 Bohr's Model Spectrum Properties of Electromagnetic Waves Atomic Nucleus and Nuclear Reactions Electromagnetic Spectrum Radioactivity 25. Ray Optics 612-055 Nuclear Fission and Fusion Reflection of Light at Plane and Spherical 29. Semiconductor Devices 751-782 Mirrors Solids and Crystals Refraction of Light at Plane Surfaces Semiconductors: p-n Junction Total Internal Reflection Transistor Lenses and Prism Digital Circuit Scattering of Light 30. Communication System 783-795 Optical Instrument Modulation and Demodulation 26. Wave Optics 656-079 Space and Line Communication Nature of Light and Huygen's Principle Lasers and Masers Interference of Light Constituents of Universe and Hubble's Law Questions Asked in JEE Main 2015 797-805 Solved Papers 2016 (JEE Main, BITSAT, AP EAMCET, TS EAMCET, GGSIPU) 1-48 Solved Papers 2017 (JEE Main & Advanced, BITSAT, VIT & WB JEE) 1-48 Solved Papers 2018 (JEE Main & Advanced, BITSAT, WB JEE & KCET) 1-47 Solved Papers 2019 (JEE Main & Advanced, BITSAT & WB JEE) 1-49 Units and Measurements QUICK REVIEW Physical Quantities Some Supplementary Quantities and their SI Units • All the quantities which can be measured directly or • Plane angle (8) at centre in radian indirectly in terms of wruch laws of physics are described = Length of arc = !.. = rad <J 8 1 and whose measurement is necessary, are called physical Radius r Length of quantities. 180° = 1t rad, circular • Physical quantities are of two types, one is fundamental arc =r 1° = 60' = 60 min quantities wruch is independent of other physical r I' = I min = 60" = 60 quantities, second one is derived quantities which can be 8 = 1 rad derived from the fundamental quantities. • The solid angle made by surface t,,.S at point O is given by Unit ~Q = Mcos0 ,J· A physical quantity is measured by comparing with certain standard amount of the same physical quantity called unit. Different systems of units MKS CGS FPS ST unit system system system Length, m Length, cm Length, ft Tt is an extended form of (metre) (centimetre) (foot) MKS system. Tt includes • It is measured in steradian. four more fundamental Mass, kg Mass, g Mass, lb • Solid angle at centre of sphere units (in addition to three (kTiliomgrea,ms ) T(gimrame,)s (Tpiomuned,s) rbeapsriecs uennitt sfu) nwdhaimche ntal Q = Area of surface of sphere= 41tR2 = 47t sr (Radius)2 R2 (second) (second) (second) quantities in electricity, basic matter quantity, heat and light. Some Derived Quantities are with SI Units • Area= (length) x (length) with unit m2. SI units of fundamental quantities • Force= (mass) x (acceleration) with unit kg-rns-2 or N. Fundamental quantities ame Symbol Commonly used derived lmits are as below : Length metre m • Joule (J) for energy or work, watt (W) for power, volt (V) Mass kilogram kg for potential difference, coulomb (C) for charge, tesla (T) Time second s for magnetic field, ohm ( Q) for resistance, etc. Electric current ampere A • The product of numerical value of the physical quantity (n) Thermodynamic temperature kelvin K and its unit (u) remains constant. Amount of substance mole mol 1.e. nu=constant n u =n u Luminous intensity candela cd ⇒ 1 1 2 2 e.g. 2. 8 m = 280 cm= 0.0028 km 2 I Chapterwise & Topicwise Engineering Entrances Solved Papers Some Important Units (Though outside SI units) Accuracy and Precision of Instrument 1 pound= 453.6 g = 0.4536 kg • The accuracy of a measurement is a measure of how close the measured value is to the true value, while precision tells l torr= 1mm of Hg= 133.3 Pa us to what resolution the quantity is measured. 1 bar= 105 Nm-2 = 105 Pa, 1 shake= 10-8 s Note For measuring mass of atoms and molecules atomic l parsec= 3.08 x 1016 m = 3.26ly mass unit, 1 amu = 1.66x 10-2 kg = (1/12) of mass of Parsec is the distance at which average radius of the earth's carbon-12, atom. orbit subtends one second angle. • A clock is used to measure time interval ( cesium clocks are 1 light year (ly) = distance covered by light is vacuum in very accurate). 1 year=9.46x 1015 m. • Smaller the least count, higher is the accuracy of measurement. 1 AU (Astronomical unit)= mean distance of the earth from the sun= 1.5x 1011m. Errors in Measurement 1 calorie= 4.2 J, l eV = 1.6 x 10-19 J, 1 year= 365.25 days • Difference in the true value and the measured value of a quantity is called error of measurement. Some Important Prefixes • Systematic errors are in one direction while random errors lm = 1000 mm, 10-2 = cm, 10-6 =micro(µ), occur irregularly and at random in magnitude and direction. 10-9 = nano (n), 10-12 = pico (p), 10-15 = femto (f), • Mean of various observations from a1, a2, ..• , an is 103 = kilo (k), 106 = mega (M), 109 = giga (G), - _a_1_ +_a_2_+_· ·_· +_a_n amean - 12 15 n 10 = tera (T), 10 = peta (P). lt,,.a l+lt,,.a I+···+ lt,,.a I Measurement • Mean absolute error, /t,,.a mean = 1 2 n n To make a measurement, the magnitude of the physical Where, /t,,.a1 =la1 - ameanl quantity is compared with the standard value of the same physical quantity. /t,,.a2 = Ia 2 - a mean I Measurement of Length There are two methods for the measurement of length as /t,,.an = Ia n - a mean I below: Direct method In this method, measurement of length • Fractional or relative error = /t,,.amean involves the use of amean (i) a metre scale (10-3 to 102 m) tia Percentage error = mean x 100 (ii) vernier calliper (upto 10-4 m) amean (iii) screw gauge and spherometer (up to 10-5m). • Error of a sum or a difference Indirect method This method is used for measurement of i.e., Z=A+B large distances like parallax method for distance of heavenly or Z = A - B is given by bodies planets, stars, etc. tiZ=M+M Least Count • Error in quantity raised to some power • Least count of instrument is smallest measurement which For Z=AaBbCc can be made with instrument. Value of 1 part on main scale(s) • Least count= Number ofp arts on vernier scale ( n) Least count of vernier calliper= 1M SD - 1V SD Significant Figures where, MSD = Main Scale Division, VSD = Vernier Scale • In a number which is the result of a measurement. The digits Division. that are known reliably plus the first uncertain digit are known as significant digits or significant figures. • Least count of screw gauge Pitch (p) • Larger the number of significant figures after the decimal point in a measurement, higher is the accuracy of the Number of parts on circular path ( n) measurement. Units and Measurements I 3 Rules for Determining Significant Figures Use of Dimensional Analysis There are many steps to determine the significant Dimensions are used to check correctness of equation. figures as below : e.g. F = mvt is incorrect (i) In multiplication or division, the final result as [F]=[MLr2], [mvt]= [MLr1T]= [ML] should retain as many significant figures as are Only same dimensions quantities can be added or subtracted. there in the original number with the least significant figures. Dimensions are used to derive fo1mulae. e.g. ( 1.2 kg) (1.325 ms-2) = 1.6 kg ms-2, e.g. For oscillating pendulum, T = k m0 lb gc -7--.8--5-0= :k:g:. = 8 x lv,.. :i k gm _3 where, k is dimensionless constant, Tis time period, m is mass of 0.001 m3 bob, I is length of pendulum and g is acceleration due to gravity. Equating dimensions on both sides (ii) In addition or subtraction, the final result should retain as many decimal places as are there in the [T]= [Mt [Lt [Lr 2t ⇒ [T]= [Ma Lb+c r 2c] number with the least decimal places. - 1 I e.g. 1.75 m + 0.2 m= 2m a = 0, b + c = 0, - 2c = I ⇒ c = -2' b = -2 \jf 2nH [·: (iii) For a number greater than I without any decimal, ⇒ T= = k = 2n,experimentally] the trailing zero (es) are insignificant e.g. the number 35700 has last two zeroes are Thus, we see that the dimensional analysis is used to establish the insignificant relation among the physical quantities. => It has only 3 significant figures. Limitations Dimensional Analysis (iv) For a number with a decimal, the trailing zero (es) are significant. The dimensional method works only ift he dependence oft he product type. The numerical constants having no dimensions can not be e.g. the number 1.2000 has last three zeroes are deduced or determined by dimensional method. significant=> it has 5 significant figures. This method works only if there are as many equations available as (v) Observe 432.70 m has five significant figures, when written as 43270 cm gives impression that it there are unknowns. Such as in mechanical quantities their is only has four significant figures. three base quantities, i.e. mass, time and length. So, dimensions of these three may be equations in the guessed relation giving at most • To remove ambiguity or mistake, measurement three equations in the exponents. should be given in scientific notation, i.e. 4.3270 x 102 m has five significant figures. Some Useful Formulae to find Dimensions Note Scientific notation of number is a x 10b. • F = ma, W = Fs, 't = r x F, where, 0< a< 10,and bis integer may be positive or • Angular momentum L = I ro, negative called order of magnitude. Stress d l f .. • --.- = mo u us o elast1c1ty, e.g. Radius of the earth= 6400000 m = 6.4 x 106 m Stram Force has order of magnitude 6. We can also say that the • Stress = --, radius of the earth is of order of 106. Area Radius of hydrogen nucleus = 1.2 x 10-15 m has • HeatQ to raise temperature by T,Q = msT, liQ KA (T. - T, ) order of magnitude= - 15. Also, radius of hydrogen • Heatflow,-= 2 1 nucleus is of the order oflo-15• fit I ' • Wave equation, y = a sin (kx-rot 1 Dimensions of a Physical Quantity 1 The dimensions of a physical quantity are powers to • Force between two charges F =- - q, q2 ' 4ne r2 ' which base or fundamental physical quantities should 0 be raised by some exponent to represent the given • Magnetic field, B = µ 01, Voltage, V = JR, derived physical quantity. 2R e.g. Force with unit N or kg - ms-2 has mass (M), • Power= VI, Charge, q = CV, di length (L) and time (T). • Induced emf, e = - L- dt Dimensions of force are expressed as below: [Force]= [MLr2] • Electric field, E = ~d and p V = Nk8 T. Force has the din1ension in mass= 1, in length= I, where all symbols have their usual meanings. in time= - 2

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