Multiple Choice Questions with Explanatory Answers - Kopykitab

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UPKAR PRAKASHAN, AGRA-2

By

Dr. Surekha Tomar

(Multiple Choice Questions with Explanatory Answers)(Multiple Choice Questions with Explanatory Answers)(Multiple Choice Questions with Explanatory Answers)(Multiple Choice Questions with Explanatory Answers)(Multiple Choice Questions with Explanatory Answers)

© Publishers

Publishers

UPKAR PRAKASHAN

(An ISO 9001 : 2000 Company)

2/11A, Swadeshi Bima Nagar, AGRA-282 002

Phone : 4053333, 2530966, 2531101

Fax : (0562) 4053330, 4031570

E-mail : care@upkar.in

Website : www.upkar.in

Branch Offices

4845, Ansari Road, Daryaganj, 1-8-1/B, R.R. Complex (Near Sundaraiah Park,

New Delhi-110 002 Adjacent to Manasa Enclave Gate), Bagh Lingampally, Phone : 011-23251844/66 Hyderabad-500 044 (A.P.), Phone : 040-66753330 ?The publishers have taken all possible precautions in publishing this book, yet if any mistake has crept in, the publishers shall not be responsible for the same.

?This book or any part thereof may not be reproduced in any form byPhotographic, Mechanical, or any other method, for any use, without writtenpermission from the Publishers.

?Only the courts at Agra shall have the jurisdiction for any legal dispute.

ISBN : 978-81-7482-137-9

Price : 599·00

(Rs. Five Hundred Ninety Nine Only)

Code No. 1569

Printed at : Upkar Prakashan (Printing Unit) Bye-pass, Agra

Preface

This book completely covers all the areas of syllabus for GATE examinations, besides teaching effective problem solving. The salient features include easy to understand explanations of problems of various competitive examinations. Infact, with the present rapid growth of the fascinating basic subject Physics, it would be quite impossible for any book, even a special treatise, to be strictly up-to-date. However, up- to-dateness is not an imperative requisite, since it is assumed that the student who wishes the latest knowledge regarding the pattern and style will consult the current periodicals. In preparing the manuscript, the author has consulted freely many very excellent books which deal with many important topics of the subject. However, in every chapter the author has shown her special skill by way of illustrations, multiple explanations of objective questions and problems. The author shall feel highly satisfied and sufficiently rewarded in case the students who will be appearing in various competitive examinations are benefited to any substantial extent. The reader, both students and teachers, are welcome to make suggestions for further improvement of the book. -Dr. Surekha Tomar

CONTENTS

?Syllabus ?General Information ?Rules and Regulations ?Patterns of Question Papers ?Multiple Choice Questions ?Important Tips ?Previous Years" Papers with Solutions

1. Basic Mathematical Methods 3-138

?Objective Type Questions 38 ?Descriptive Questions 101

2. Classical Dynamics 139-209

?Objective Type Questions 148 ?Descriptive Questions 185

3. Electromagnetics 210-313

?Objective Type Questions 224 ?Descriptive Questions 285

4. Quantum Physics andApplication 314-424

?Objective Type Questions 330 ?Descriptive Questions 388

5. Thermodynamics and

Statistical Physics 425-534

?Objective Type Questions 440 ?Descriptive Questions 493

6. Electronics 535-700

?Objective Type Questions 570 ?Objective Type Questions(Digital Electronics) 615 ?Descriptive Questions 637

7. Experimental Techniquesand Data Analysis 701-759

?Objective Type Questions 717 ?Descriptive Questions 741

8. Atomic and MolecularPhysics 760-853

?Objective Type Questions 771 ?Descriptive Questions 797

9. Condensed Matter Physics 854-945

?Objective Type Questions 867 ?Descriptive Questions 907

10. Nuclear and ParticlePhysics 946-1033

?Objective Type Questions 964 ?Descriptive Questions 986 ?Descriptive Questions (Particle Physics) 1024 ?Model Paper-1 1034-1048 ?Model Paper-2 1049-1064

SYLLABUS

Mathematical Physics-Linear vector space,

matrices; vector calculus; linear differential equations; elements of complex analysis; Laplace transforms, Fourier analysis, elementary ideas about tensors.

Classical Mechanics-Conservation laws;

Central forces; Kepler problem and planetary

motion; collisions and scattering in laboratory and centre of mass frames; mechanics of system of particles; rigid body dynamics; moment of inertia tensor; non-inertial frames and pseudo forces; variational principle; Lagrange"s and Hamilton"s formalisms; equation of motion, cyclic co- ordinates, Poisson bracket; periodic motion, small oscillations, normal modes; special theory of relativity-Lorentz transformations, relativistic kinematics, mass-energy equivalence.

Electromagnetic Theory-Solution of

electrostatic and magnetostatic problems including boundary value problems; dielectrics and conductors; Biot-Savart"s and Ampere"s laws; Faraday"s law; Maxwell"s equations; scalar and vector potentials; Coulomb and Lorentz gauges; Electromagnetic waves and their reflection, refraction, interference, diffraction and polarization. Poynting vector, Poynting theorem, energy and momentum of electromagnetic waves; radiation from a moving charge.

Quantum Mechanics-Physical basis of

quantum mechanics; uncertainty principle;

Schrodinger equation; one, two and three

dimensional potential problems; particle in a box, harmonic oscillator, hydrogen atom; linear vectors and operators in Hilbert space; angular momentum and spin; addition of angular momenta; time independent perturbation theory; elementary scattering theory.

Thermodynamics and Statistical Physics-

Laws of thermodynamics; macrostates and micro-

states, phase space; probability ensembles; parti- tion function, free energy, calculation of thermodynamic quantities; classical and quantumstatistics; degenerate Fermi gas; black body radiation and Planck"s distribution law; Bose-

Einstein condensation; first and second order

phase transitions, critical point.

Atomic and Molecular Physics-Spectra of

one-and many-electron atoms; LS and jj coupling; hyperfine structure; Zeeman and Stark effects; electric dipole transitions and selection rules; X- ray spectra; rotational and vibrational spectra of diatomic molecules; electronic transition in diatomic molecules, Franck-Condon principle;

Raman effect; NMR and ESR; lasers.

Solid State Physics-Elements of crystallo-

graphy; diffraction methods for structure determination; bonding in solids; elastic properties of solids; defects in crystals; lattice vibrations and thermal properties of solids; free electron theory; band theory of solids; metals, semi-conductors and insulators; transport properties; optical, dielectric and magnetic properties of solids; elements of superconductivity.

Nuclear and Particle Physics-Nuclear radii

and charge distributions, nuclear binding energy,

Electric and magnetic moments; nuclear models,

liquid drop model-semi-empirical mass formula,

Fermi gas model of nucleus, nuclear shell model;

nuclear force and two nucleon problem; Alpha- decay, Beta-decay, electromagnetic transitions in nuclei; Rutherford scattering, nuclear reactions conservation laws; fission and fusion; particle accelerators and detectors; elementary particles, photons, baryons, mesons and leptons; quark model.

Electronics-Network analysis; semi-condu-

ctor devices; bipolar junction transistors, Field

Effect Transistors, amplifier and oscillator cir-

cuits; operational amplifier, negative feedback circuits, active filters and oscillators; rectifier circuits, regulated power supplies; basic digital logic circuits, sequential circuits, flip-flops, counters, registers, A/D and D/A conversion.

GENERAL INFORMATION

The Graduate Aptitude Test in Engineering (GATE) is an All-India Examination administered and conducted jointly by the Indian Institute of Science, Bangalore and seven Indian Institutes of Technology on behalf of the National Co-ordination Board-GATE, Department of Higher Education, Ministry of Human Resources Development (MHRD), Government of India. GATE is conducted through the constitution of eight zones. The zones and the corresponding administering institutes are :

Zone 1 - Indian Institute of Science, Bengaluru.

Zone 2 - Indian Institute of Technology, Bombay.

Zone 3 - Indian Institute of Technology, Delhi.

Zone 4 - Indian Institute of Technology, Guwahati.

Zone 5 - Indian Institute of Technology, Kanpur.

Zone 6 - Indian Institute of Technology, Kharagpur.

Zone 7 - Indian Institute of Technology, Chennai.

Zone 8 - Indian Institute of Technology, Roorkee.

OBJECTIVES OF GATE

*Identify, at the National level, meritorious and motivated candidates for admission to Postgraduate

Programmes in Engineering, Technology, Architecture, Science and Pharmacy. *Serve as a mandatory qualification for the MHRD scholarship/assistantship. *Serve as benchmark of normalization of the Undergraduate Engineering Education in the country.

CONTACT DETAILS OF THE ZONAL GATE OFFICES

Examination Cities for Offline Exam. Address of the

Chairman, GATE of

the corresponding zoneTelephone, Fax and e- mail

Zone 1

Ananthapur, Bagalkot, Belgaum, Bengaluru,

Davangere, Hassan, Hubli , Hyderabad,

Kurnool, Mahabubnagar, Mangalore, Mysore,

Secunderabad and SurathkalChairman, GATE

Indian Institute of

Science, Bengaluru

Bangalore-560 012Phone : 080-2293 2392

Fax : 080-2360 1227

e-mail : gate@gate.iisc.ernet.in

Zone 2

Ahmedabad, Ahmednagar, Akola, Amravati,

Aurangabad, Bhusawal, Goa, Gondia, Gulbarga,

Jalgaon, Kolhapur, Latur, Lonavala, Loni,

Mahesana, Mumbai, Nagpur, Nanded, Nashik,

Navi Mumbai, Pandharpur, Pune, Rajkot,

Sangli, Satara, Shegaon, Solapur, Surat, Thane,

Vadodara, and WardhaChairman, GATE

Indian Institute of

Technology Bombay

Powai,

Mumbai-400 076Phone : 022-2576 7068

Fax : 022-2572 3706

e-mail : gateoffice@iitb.ac.in

Zone 3

Ajmer, Alwar, Bikaner, Delhi Central, Delhi

East, Delhi North, Delhi South, Delhi West,

Faridabad, Gurgaon, Indore, Jaipur, Jammu,

Jodhpur, Sikar, Udaipur, and UjjainChairman, GATE

Indian Institute of

Technology Delhi

Hauz Khas

New Delhi-110 016Phone : 011-2659 1749

Fax : 011-2658 1579

e-mail : gateoffice@admin.iitd. ac.in ( viii )

Zone 4

Agartala, Asansol, Bhagalpur, Dhanbad,

Durgapur, Gangtok, Guwahati, Imphal,

Itanagar, Jorhat, Kalyani, Patna, Silchar,

Siliguri, and TezpurChairman, GATE

Indian Institute of

Technology, Guwahati

North Guwahati

Guwahati-781 039Phone : 0361-258 2751

Fax : 0361-2582755

e-mail : gate@iitg.ernet.in

Zone 5

Agra, Aligarh, Allahabad, Bareilly, Bhopal,

Gorakhpur, Gwalior, Jabalpur, Jhansi, Kanpur,

Lucknow, Saugar (Sagar, MP), Sultanpur and

VaranasiChairman, GATE

Indian Institute of

Technology, Kanpur

Kanpur-208 016Phone : 0512-259 7412

Fax : 0512-259 0932

e-mail : gate@iitk.ac.in

Zone 6

Balasore, Berhampur (Orissa), Bhimavaram,

Bhubaneswar, Bilaspur, Cuttack, Eluru,

Jamshedpur, Kakinada (AP), Kharagpur,

Kolkata, Machilipatnam, Raipur, Rajahmundry,

Ranchi, Rourkela, Sambalpur, Srikakulam,

Tadepalligudem, Vijayawada and

VisakhapatnamChairman, GATE

Indian Institute of

Technology Kharagpur

Kharagpur-721 302Phone : 03222-282091

Fax : 03222-278243

e-mail : gate@adm.iitkgp.ernet.in

Zone 7

Bapatla, Chennai North, Chennai South,

Chidambaram, Chittoor, Coimbatore, Dindigul,

Ernakulam, Gudur, Guntur, Kadapa, Kannur

(Kerala), Karimnagar, Khammam, Kollam,

Kothagudem, Kottayam, Kozhikode, Madurai,

Manchiryal, Nagercoil, Nalgonda, Nellore,

Ongole, Palakkad, Puducherry(Pondicherry),

Salem, Tenali, Thanjavur, Thiruvananthapuram,

Thrissur, Tiruchirapalli, Tirunelveli, Tirupati

and WarangalChairman, GATE

Indian Institute of

Technology Madras

Chennai-600 036Phone : 044-2257 8200

Fax : 044-2257 8204

e-mail : gate@iitm.ac.in

Zone 8

Amritsar, Bathinda, Bijnor, Chandigarh,

Dehradun, Ghaziabad, Haldwani, Hamirpur

(HP), Haridwar, Hisar, Jalandhar, Kota,

Kurukshetra, Ludhiana, Mathura, Meerut,

Muzaffarnagar, Noida, Patiala, Rohtak,

Roorkee, Shimla and YamunanagarChairman, GATE

Indian Institute of

Technology Roorkee

Roorkee-247 667Phone : 01332-284531

Fax: 01332-285707

e-mail: gate@iitr.ernet.in

STRUCTURE OF GATE

A candidate can apply for only ONE of the 21 papers listed in Table. The syllabi of all the

papers are given in the GATE websites of IISc and IITs. Making a choice of the appropriate paper is the

responsibility of the candidate. Some guidelines in this respect are suggested below. The candidate is expected to appear in a paper appropriate to the discipline of his/her qualifying degree. The candidate is, however, free to choose any paper according to his/her admission plan,

keeping in mind the eligibility criteria of the institutions in which he/she wishes to seek admission.

( ix ) GATE examination will have the following 21 papers :

Paper Code Paper Code

Aerospace Engg. AEGeology & Geophysics GG

Agricultural Engg. AG Instrumentation Engg. IN

Architecture and Planning AR Mathematics MA

Biotechnology BT Mechanical Engg. ME

Civil Engg. CE Mining Engg. MN

Chemical Engg. CH Metallurgical Engg. MT

Computer Science & Information

TechnologyCS Physics

Production & Industrial Engg.PH

PI

Chemistry CY Textile Engg. & Fibre Science TF

Electronics & Communication Engg. EC Engineering Sciences XE

Electrical Engg. EE Life Sciences XL

Papers XE and XL are of general nature and will comprise the following Sections :

Engineering Sciences (XE) Life Sciences (XL)

Section Code Section Code

Engg. Mathematics (Compulsory) (A) Chemistry (Compulsory) (H)

Fluid Mechanics (B) Biochemistry (I)

Materials Science (C) Botany (J)

Solid Mechanics (D) Microbiology (K)

Thermodynamics(E) Zoology (L)

Polymer Science and Engineering(F) Food Technology (M)

Food Technology(G)

Candidates appearing in XE or XL papers are required to answer three sections apart from the General Aptitude (GA) questions. Sections (A) and (H) are compulsory in XE and XL respectively. Candidates can choose any two out of the remaining sections mentioned against the respective papers. ONLINE Examination: Examination using computers where the candidate will choose the correct answer out of four options or fill in the numerical answer using mouse. OFFLINE Examination: Examination where the candidate will mark the correct answer out of four options in an Optical Response Sheet (ORS) by darkening the appropriate bubble.

EXAMINATION TYPE

The GATE examination consists of a single paper of 3 hours duration which contains 65 questions carrying a maximum of 100 marks. The question paper will consist of only objective questions. The pattern of question papers is given in Section 4. The examination for the papers with codes AE, AG, AR, GG, MN and TF will be carried out ONLINE using computers where the candidates will be

required to enter the answer for each question using mouse. For all other papers, the candidates will

have to mark the correct choice on an Optical Response Sheet (ORS) by darkening the appropriate bubble against each question. There will be negative marking for each wrong answer, except for some questions, as explained in Section 4. Each GATE paper shall have a General Aptitude (GA) component carrying 15 marks.