GATE Solved Question Papers for Physics [PH] by AglaSem.Com

SOLVED PAPERS

GATEPHYSICS (PH)

aglaem.comA comprehensive study guide for GATE

CONTENTS

Introduction Question Paper Pattern Design of Questions Marking Scheme Syllabus Previous Year Solved Papers

o Solved Question Paper 2014o Answer Key 2014o Solved Question Paper 2013o Answer Key 2013o Solved Question Paper 2012o Answer Key 2012

IntroductionThe Graduate Aptitude Test in Engineering (GATE) is the all India level examinationconducted by the Indian Institute of Science and seven Indian Institutes of Technology(IITs).

A crucial part of GATE preparation is to solve and practice using previous year GATEpapers. Solving previous year GATE papers help the candidate in understanding the exampattern, knowing the level of difficulty of questions, and analyzing preparation.

While attempting to solve any previous year GATE paper, it is advisable that it is done in asimulated test environment. This means, that the candidate sets a timer to countdown totest time, makes sure there is no other distraction, and then sits down to take the test as ifhe / she is in the exam hall. After attempting the paper, check how many questions youcould get right in the first attempt. Analyse the strong and weak areas of preparation, andaccordingly devise a study schedule or revision pattern. After going through those areaswhere in the first attempt could not do well, try the next paper.

Almost all of the engineering colleges in India take admission in M.Tech courses on thebasis of GATE scores. Apart from that, PSUs also recruit students directly on this basis.

To score high in this elite examination is tough, but quite achievable.

GATE Previous Year Solved Papers by_________________________________________________________

Question Paper PatternIn all the papers, there will be a total of 65 questions carrying 100 marks, out of which 10questions carrying a total of 15 marks are in General Aptitude (GA).

In the papers bearing the codes AE, AG, BT, CE, CH, CS, EC, EE, IN, ME, MN, MT, PI, TF andXE, the Engineering Mathematics will carry around 13% of the total marks, the GeneralAptitude section will carry 15% of the total marks and the remaining percentage of thetotal marks is devoted to the subject of the paper.

In the papers bearing the codes AR, CY, EY, GG, MA, PH and XL, the General Aptitudesection will carry 15% of the total marks and the remaining 85% of the total marks isdevoted to the subject of the paper.

GATE would contain questions of two different types in various papers:

(i) Multiple Choice Questions (MCQ) carrying 1 or 2 marks each in all papers andsections. These questions are objective in nature, and each will have a choice of fouranswers, out of which the candidate has to mark the correct answer(s).

(ii) Numerical Answer Questions of 1 or 2 marks each in all papers and sections. Forthese questions the answer is a real number, to be entered by the candidate using thevirtual keypad. No choices will be shown for this type of questions.

GATE Previous Year Solved Papers by________________________________________________________

Design of QuestionsThe questions in a paper may be designed to test the following abilities:

(i) Recall: These are based on facts, principles, formulae or laws of the discipline of thepaper. The candidate is expected to be able to obtain the answer either from his/hermemory of the subject or at most from a one-line computation.

(ii) Comprehension: These questions will test the candidate's understanding of thebasics of his/her field, by requiring him/her to draw simple conclusions from fundamentalideas.

(iii) Application: In these questions, the candidate is expected to apply his/herknowledge either through computation or by logical reasoning.

(iv) Analysis and Synthesis: In these questions, the candidate is presented with data,diagrams, images etc. that require analysis before a question can be answered. A Synthesisquestion might require the candidate to compare two or more pieces of information.Questions in this category could, for example, involve candidates in recognising unstatedassumptions, or separating useful information from irrelevant information.

GATE Previous Year Solved Papers by__________________________________________________________

Marking SchemeFor 1-mark multiple-choice questions, 1/3 marks will be deducted for a wrong answer.Likewise, for2-marks multiple-choice questions, 2/3 marks will be deducted for a wronganswer. There is no negative marking for numerical answer type questions.

General Aptitude (GA) Questions

In all papers, GA questions carry a total of 15 marks. The GA section includes 5 questionscarrying 1 mark each (sub-total 5 marks) and 5 questions carrying 2 marks each (sub-total10 marks).

Question Papers other than GG, XE and XL

These papers would contain 25 questions carrying 1 mark each (sub-total 25 marks) and30 questions carrying 2 marks each (sub-total 60 marks). The question paper will consist ofquestions of multiple choice and numerical answer type. For numerical answer questions,choices will not be given. Candidates have to enter the answer (which will be a realnumber, signed or unsigned, e.g. 25.06, -25.06, 25, -25 etc.) using a virtual keypad. Anappropriate range will be considered while evaluating the numerical answer typequestions so that the candidate is not penalized due to the usual round-off errors.

GG (Geology and Geophysics) Paper

Apart from the General Aptitude (GA) section, the GG question paper consists of two parts:Part A and Part B. Part A is common for all candidates. Part B contains two sections: Section1 (Geology) and Section 2 (Geo-physics). Candidates will have to attempt questions in PartA and either Section 1 or Section 2 in Part B.

Part A consists of 25 multiple-choice questions carrying 1-mark each (sub-total 25 marksand some of these may be numerical answer type questions). Each section in Part B(Section 1 and Section 2) consists of 30 multiple choice questions carrying 2 marks each(sub-total 60 marks and some of these may be numerical answer type questions).

XE Paper (Engineering Sciences)


In XE paper, Engineering Mathematics section (Section A) is compulsory. This sectioncontains 11 questions carrying a total of 15 marks: 7 questions carrying 1 mark each (sub-total 7 marks), and 4 questions carrying 2 marks each (sub-total 8 marks). Some questionsmay be of numerical answer type questions.

Each of the other sections of the XE paper (Sections B through G) contains 22 questionscarrying a total of 35 marks: 9 questions carrying 1 mark each (sub-total 9 marks) and 13questions carrying 2 marks each (sub-total 26 marks). Some questions may be ofnumerical answer type.

XL Paper (Life Sciences)

In XL paper, Chemistry section (Section H) is compulsory. This section contains 15questions carrying a total of 25 marks: 5 questions carrying 1 mark each (sub-total 5 marks)and 10 questions carrying 2-marks each (sub-total 20 marks). Some questions may be ofnumerical answer type.

Each of the other sections of the XL paper (Sections I through M) contains 20 questionscarrying a total of 30 marks: 10 questions carrying 1 mark each (sub-total 10 marks) and 10questions carrying 2 marks each (sub-total 20 marks). Some questions may be ofnumerical answer type.

Note on Negative Marking for Wrong Answers

For a wrong answer chosen for the multiple choice questions, there would be negativemarking. For1-mark multiple choice questions, 1/3 mark will be deducted for a wronganswer. Likewise, for 2-mark multiple choice questions, 2/3 mark will be deducted for awrong answer. However, there is no negative marking for a wrong answer in numericalanswer type questions.


Syllabus for General Aptitude (GA)Verbal Ability: English grammar, sentence completion, verbal analogies, word groups,instructions, critical reasoning and verbal deduction.

Numerical Ability: Numerical computation, numerical estimation, numerical reasoningand data interpretation.

Syllabus for Physics (PH)Mathematical Physics: Linear vector space; matrices; vector calculus; linear differentialequations; elements of complex analysis; Laplace transforms, Fourier analysis, elementaryideas about tensors.

Classical Mechanics: Conservation laws; central forces, Kepler problem and planetarymotion; collisions and scattering in laboratory and centre of mass frames; mechanics ofsystem of particles; rigid body dynamics; moment of inertia tensor; noninertial frames andpseudo forces; variational principle; Lagranges and Hamiltons formalisms; equation ofmotion, cyclic coordinates, Poisson bracket; periodic motion, small oscillations, normalmodes; special theory of relativity Lorentz transformations, relativistic kinematics, mass-energy equivalence.

Electromagnetic Theory: Solution of electrostatic and magneto static problems includingboundary value problems; di electrics and conductors; Biot-Savarts and Amperes laws;Faradays law; Maxwells equations; scalar and vector potentials; Coulomb and Lorentzgauges; Electromagnetic waves and their reflection, refraction, interference, diffractionand polarization. Poynting vector, Poynting theorem, energy and momentum ofelectromagnetic 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 abox, harmonic oscillator, hydrogen atom; linear vectors and operators in Hilbert space;angular momentum and spin; addition of angular momenta; time independentperturbation theory; elementary scattering theory.

GATE Previous Year Solved Papers by_______________________________________________________________

Thermodynamics and Statistical Physics: Laws of thermodynamics; macrostates andmicrostates; phase space; probability ensembles; partition function, free energy,calculation of thermodynamic quantities; classical and quantum statistics; degenerateFermi gas; black body radiation and Plancks 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 jjcoupling; hyperfine structure; Zeeman and Stark effects; electric dipole transitions andselection rules; X-ray spectra; rotational and vibrational spectra of diatomic molecules;electronic transition in diatomic molecules, Franck-Condon principle; Raman effect; NMRand ESR; lasers.

Solid State Physics: Elements of crystallography; diffraction methods for structuredetermination; bonding in solids; elastic properties of solids; defects in crystals; latticevibrations and thermal properties of solids; free electron theory; band theory of solids;metals, semiconductors and insulators; transport properties; optical, dielectric andmagnetic properties of solids; elements of superconductivity.

Nuclear and Particle Physics: Nuclear radii and charge distributions, nuclear bindingenergy, Electric and magnetic moments; nuclear models, liquid drop model semi-empirical mass formula, Fermi gas model of nucleus, nuclear shell model; nuclear forceand two nucleon problem; Alpha decay, Beta-decay, electromagnetic transitions innuclei;Rutherford scattering,nuclear reactions, conservation laws; fission andfusion;particle accelerators and detectors; elementary particles, photons, baryons, mesonsand leptons; quark model.

Electronics: Network analysis; semiconductor devices; Bipolar Junction Transistors, FieldEffect Transistors, amplifier and oscillator circuits; operational amplifier, negative feedbackcircuits ,active filters and oscillators; rectifier circuits, regulated power supplies; basicdigital logic circuits, sequential circuits, flip-flops, counters, registers, A/D and D/Aconversion.


GATEPrevious Year Solved Papers

Physics - PH

2012 - 14


Duration: 180 minutes Maximum Marks: 100

Read the following instructions carefully.

1. To login, enter your Registration Number and password provided to you. Kindly go through the various symbols used in the test and understand their meaning before you start the examination.

2. Once you login and after the start of the examination, you can view all the questions in the question paper, by clicking on the View All Questions button in the screen.

3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject specific GATE paper for 85 marks. Both these sections are compulsory. The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question numbers 6 to 10 are of 2-mark each. The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to 25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each.

4. Depending upon the GATE paper, there may be useful common data that may be required for answering the questions. If the paper has such useful data, the same can be viewed by clicking on the Useful Common Data button that appears at the top, right hand side of the screen.

5. The computer allotted to you at the examination center runs specialized software that permits only one answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for the numerical answer type questions using the virtual keyboard and mouse.

6. Your answers shall be updated and saved on a server periodically and also at the end of the examination. The examination will stop automatically at the end of 180 minutes.

7. In each paper a candidate can answer a total of 65 questions carrying 100 marks. 8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer

type. 9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the

correct answer. The candidate has to choose the correct answer by clicking on the bubble () placed before the choice.

10. For numerical answer type questions, each question will have a numerical answer and there will not be any choices. For these questions, the answer should be enteredby using the virtual keyboard that appears on the monitor and the mouse.

11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong answer will result in deduction of marks for a 1-mark question and marks for a 2-mark question.

12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE.

13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination centre for all your rough work. The Scribble Pad has to be returned at the end of the examination.

Declaration by the candidate:

I have read and understood all the above instructions. I have also read and understood clearly the instructions given on the admit card and shall follow the same. I also understand that in case I am found to violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of the examination all the computer hardware allotted to me are in proper working condition.

GATE 2014 Solved Paper PH: Physics

GATE Previous Year Solved Papers by______________________________________________________________

Q. 1 Q. 5 carry one mark each. Q.1 A student is required to demonstrate a high level of comprehension of the subject, especially in the

social sciences.

The word closest in meaning to comprehension is

(A) understanding (B) meaning (C) concentration (D) stability

Q.2 Choose the most appropriate word from the options given below to complete the following sentence.

One of his biggest ______ was his ability to forgive.

(A) vice (B) virtues (C) choices (D) strength

Q.3 Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently.

Which one of the statements below is logically valid and can be inferred from the above sentences?

(A) Rajan has decided to work only in a group. (B) Rajan and Sajan were formed into a group against their wishes. (C) Sajan had decided to give in to Rajans request to work with him. (D) Rajan had believed that Sajan and he would be working together.

Q.4 If y = 5x2 + 3, then the tangent at x = 0, y = 3 (A) passes through x = 0, y = 0 (B) has a slope of +1 (C) is parallel to the x-axis (D) has a slope of 1

Q.5 A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes?

Q. 6 Q. 10 carry two marks each.

Q.6 Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK (A) ALRVX (B) EPVZB (C) ITZDF (D) OYEIK

Q.7 Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors below Faisals floor. Dilip does not live on floor number 2. Eswar does not live on a floor immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the following floor-person combinations is correct?

Anuj Bhola Chandan Dilip Eswar Faisal (A) 6 2 5 1 3 4 (B) 2 6 5 1 3 4 (C) 4 2 6 3 1 5 (D) 2 4 6 1 3 5

GATE Previous Year Solved Papers by

GATE 2014 General Aptitude - GA

Q.8 The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?

Q.9 One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft?

(A) 3.0 (B) 2.5 (C) 1.5 (D) 1.25

Q.10 The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? (k percentile is the value such that k percent of the data fall below that value)

(i) On average, it rains more in July than in December (ii) Every year, the amount of rainfall in August is more than that in January (iii) July rainfall can be estimated with better confidence than February rainfall (iv) In August, there is at least 500 mm of rainfall (A) (i) and (ii) (B) (i) and (iii) (C) (ii) and (iii) (D) (iii) and (iv)

END OF THE QUESTION PAPER


GATE 2014 General Aptitude - GA

Some Useful Constants

Speed of light in free space = 3 108 / Boltzmann constant = 1.380 1023 / Plancks constant = 6.626 1034 . Electron charge = 1.602 1019 Permittivity of free space 0 = 8.854 1012 2/.2 Permeability of free space 0 = 4 107 / Mass of electron me = 9.31 10-31 kg Mass of proton 271067.1 =pm kg Mass of neutron mn = 1.675 10-27 kg


GATE 2014 Physics - PH

Q. 1 Q. 25 carry one mark each. Q.1 The unit vector perpendicular to the surface 3222 =++ zyx at the point ( )1,1,1 is

(A) 3

zyx + (B)

3 zyx

(C) 3

zyx + (D)

3 zyx ++

Q.2 Which one of the following quantities is invariant under Lorentz transformation? (A) Charge density (B) Charge (C) Current (D) Electric field

Q.3 The number of normal Zeeman splitting components of 1P 1D transition is (A) 3 (B) 4 (C) 8 (D) 9

Q.4 If the half-life of an elementary particle moving with speed 0.9c in the laboratory frame is 8105 s, then the proper half-life is __________ 10-8 s. ( = 3 108 /)

Q.5 An unpolarized light wave is incident from air on a glass surface at the Brewster angle. The angle between the reflected and the refracted wave is

(A) 00 (B) 045 (C) 090 (D) 0120

Q.6 Two masses m and 3m are attached to the two ends of a massless spring with force constant K. If m = 100 g and K = 0.3 N/m, then the natural angular frequency of oscillation is ___________ Hz.

Q.7 The electric field of a uniform plane wave propagating in a dielectric, non-conducting medium is given by, ( )ztxE 4.0106cos10 7 =

V/m. The phase velocity of the wave is ________________ 108 m/s.

Q.8 The matrix

+=11

113

1i

iA

is

(A) orthogonal (B) symmetric (C) anti-symmetric (D) unitary

Q.9 The recoil momentum of an atom is Ap when it emits an infrared photon of wavelength 1500 nm, and it is Bp when it emits a photon of visible wavelength 500 nm. The ratio

B

A

pp

is

(A) 1:1 (B) 3:1 (C) 3:1 (D) 2:3

Q.10 For a gas under isothermal conditions, its pressure P varies with volume V as 3/5 VP . The bulk modulus B is proportional to

(A) 2/1V (B) 3/2V (C) 5/3V (D) 3/5V

Q.11 Which one of the following high energy processes is allowed by conservation laws? (A) 00 ++ pp (B) np ++ 0 (C) eepn ++ (D) + ++ e



Q.12 The length element ds of an arc is given by, ( ) ( ) 2122212 32)( dxdxdxdxds ++= .The metric tensor ijg is

(A)

1332

(B)

123

232

(C)

23

23

12

(D)

223

231

Q.13 The ground state and the first excited state wave functions of a one dimensional infinite potential well are 1 and 2, respectively. When two spin-up electrons are placed in this potential, which one of the following, with x1 and x2 denoting the position of the two electrons, correctly represents the space part of the ground state wave function of the system?

(A) [ ])()()()(2

122211211 xxxx (B) [ ])()()()(2

112212211 xxxx +

(C) [ ])()()()(2

122211211 xxxx + (D) [ ])()()()(2

112212211 xxxx

Q.14 If the vector potential ,32 zzyyxxA +=

satisfies the Coulomb gauge, the value of the constant is ___________________ .

Q.15 At a given temperature, T, the average energy per particle of a non-interacting gas of two-dimensional classical harmonic oscillators is ________________ kBT (kB is the Boltzmann constant).

Q.16 Which one of the following is a fermion? (A) particle (B) 4Be7 nucleus (C) Hydrogen atom (D) Deuteron

Q.17 Which one of the following three-quark states (qqq), denoted by X, CANNOT be a possible baryon? The corresponding electric charge is indicated in the superscript.

(A) X + + (B) X + (C) X (D) X

Q.18 The Hamiltons canonical equations of motion in terms of Poisson Brackets are (A) = {,} ; = {,} (B) = {, } ; = {,} (C) = {,} ; = {, } (D) = {,} ; = {,}

Q.19 The Miller indices of a plane passing through the three points having coordinates (0,0,1),(1,0,0), 1

2,

1

2,

1

4 are

(A) (212) (B) (111) (C) (121) (D) (211)



Q.20 The plot of specific heat versus temperature across the superconducting transition temperature () is most appropriately represented by

(A)

(B)

(C)

(D)

Q.21 If is the orbital angular momentum and is the spin angular momentum, then . does NOT commute with

(A) (B) 2 (C) 2 (D) + 2

T

Cp

Cp

T Cp

T

Cp

T



Q.22 The energy, for band electrons as a function of the wave vector, in the first Brillouin zone ( ) of a one dimensional monatomic lattice is shown as ( is lattice constant)

The variation of the group velocity is most appropriately represented by (A)

(B)

(C)

(D)

Q.23 For a free electron gas in two dimensions, the variation of the density of states, () as a function of energy E, is best represented by

(A)

(B)

(C)

(D)

N(E)

E

N(E)

E

N(E)

E

N(E)

E

O /a -/a

/a -/a O

k

/a -/a O

k

/a -/a O k

/a -/a O

k



Q.24 The input given to an ideal OP-AMP integrator circuit is

The correct output of the integrator circuit is

(A)

(B)

(C)

(D)

Q.25 The minimum number of flip-flops required to construct a mod-75 counter is _______.

V

t t0

V0

V

t

V0

t0

V

t

V0

t0

V

t

V0

t0

V

t t0

V0



Q. 26 Q. 55 carry two marks each. Q.26 A bead of mass m can slide without friction along a massless rod kept at 450 with the vertical as

shown in the figure. The rod is rotating about the vertical axis with a constant angular speed . At any instant, r is the distance of the bead from the origin. The momentum conjugate to r is

(A) rm (B) rm 2

1

(C) rm 21

(D) rm2

Q.27 An electron in the ground state of the hydrogen atom has the wave function () = 103 0 where 0 is constant. The expectation value of the operator 22 rzQ = , where cosrz = is (Hint: = ()+1 = (1)!+10 ) (A) 02/2 (B) 02 (C) 302/2 (D) 202

Q.28 For Nickel, the number density is 8 1023 /3 and electronic configuration is 1s22s22p63s23p63d84s2. The value of the saturation magnetization of Nickel in its ferromagnetic state is _________________ 109 /. (Given the value of Bohr magneton = 9.21 1021 2)

Q.29 A particle of mass m is in a potential given by

,

3)( 3

20

r

ar

r

arV +=

where a and r0 are positive constants. When disturbed slightly from its stable equilibrium position, it undergoes a simple harmonic oscillation. The time period of oscillation is

(A) a

mr

22

30 (B)

a

mr302 (C) a

mr3022 (D) a

mr304

Q.30 The donor concentration in a sample of n-type silicon is increased by a factor of 100. The shift in the position of the Fermi level at 300K, assuming the sample to be non degenerate is __________ meV. ( = 25 at 300 )

Q.31 A particle of mass is subjected to a potential, (,) = 122(2 + 2), ,

The state with energy 4 is -fold degenerate. The value of is ___________ .

r 450

m



Q.32 A hydrogen atom is in the state = 8

21200 37 310 + 421 321 ,

where , , in denote the principal, orbital and magnetic quantum numbers, respectively. If is the angular momentum operator, the average value of 2 is ______________ 2.

Q.33 A planet of mass m moves in a circular orbit of radius r0 in the gravitational potential () = , where k is a positive constant. The orbital angular momentum of the planet is

(A) kmr02 (B) kmr02 (C) kmr0 (D) kmr0

Q.34 The moment of inertia of a rigid diatomic molecule A is 6 times that of another rigid diatomic molecule B. If the rotational energies of the two molecules are equal, then the corresponding values of the rotational quantum numbers JA and JB are

(A) JA = 2, JB = 1 (B) JA = 3, JB = 1 (C) JA = 5, JB = 0 (D) JA = 6, JB = 1

Q.35 The value of the integral

dze

z

Cz +1

2

,

where C is the circle 4=z , is (A) i2 (B) i22 (C) i34 (D) i24

Q.36 A ray of light inside Region 1 in the xy- plane is incident at the semicircular boundary that carries no free charges. The electric field at the point ( )0 , / 4P r in plane polar coordinates is

1 7 3 rE e e=

, where andr

e e are the unit vectors. The emerging ray in Region 2 has the

electric field 2E

parallel to x- axis. If 1 2 and are the dielectric constants of Region 1 and Region 2 respectively, then 2

1

is ____________________________



Q.37 The solution of the differential equation

022

= ytdyd

,

subject to the boundary conditions ( ) 10 =y and ( ) 0=y , is (A) cos t + sin t (B) cosh t + sinh t (C) cos t - sin t (D) cosh t - sinh t

Q.38 Given that the linear transformation of a generalized coordinate q and the corresponding momentum p,

Q = q + 4ap P = q + 2p

is canonical, the value of the constant a is ___________ .

Q.39 The value of the magnetic field required to maintain non-relativistic protons of energy 1 MeV in a circular orbit of radius 100 mm is ______________ Tesla. (Given: 271067.1 =pm kg, = 1.6 1019 )

Q.40 For a system of two bosons, each of which can occupy any of the two energy levels 0 and , the mean energy of the system at a temperature T with

TkB1= is given by

(A)

2

2

212

+++

ee

ee (B)

22

1

++

ee

e

(C)

2

2

22

+++

ee

ee (D)

2

2

22

+++

ee

ee

Q.41 In an interference pattern formed by two coherent sources, the maximum and the minimum of the intensities are 9I0 and I0, respectively. The intensities of the individual waves are (A) 3I0 and I0 (B) 4I0 and I0 (C) 5I0 and 4I0 (D) 9I0 and I0

Q.42 1 and 2 are two orthogonal states of a spin 21 system. It is given that

+

=

10

32

01

31

1 ,

where

01

and

10

represent the spin-up and spin-down states, respectively. When the system is

in the state 2, its probability to be in the spin-up state is ______________ .

Q.43 Neutrons moving with speed 103 m/s are used for the determination of crystal structure. If the Bragg angle for the first order diffraction is 300, the interplanar spacing of the crystal is _________ . (Given: mn = 1.675 10-27 kg, = 6.626 1034 . )



Q.44 The Hamiltonian of a particle of mass m is given by

2 2

2 2H

p qm

= . Which one of the following figures describes the motion of the particle in phase space?

(A)

(B)

(C) (D)

Q.45 The intensity of a laser in free space is 150 mW/m2. The corresponding amplitude of the electric field of the laser is ____________ V/m. (0 = 8.854 1012 2/.2)

Q.46 The emission wavelength for the transition 1D2 1F3 is 3122 . The ratio of populations of the final to the initial states at a temperature 5000 K is ( = 6.626 1034 . , = 3 108 /, = 1.380 1023 /) (A) 2.03 10-5 (B) 4.02 10-5 (C) 7.02 10-5 (D) 9.83 10-5

Q.47 Consider a system of 3 fermions, which can occupy any of the 4 available energy states with equal probability. The entropy of the system is

(A) ln2 (B) 2ln2 (C) 2ln4 (D) 3ln4

Q.48 A particle is confined to a one dimensional potential box with the potential ( )otherwise, 0,0

=

Q.50 A one dimensional harmonic oscillator is in the superposition of number states, n , given by

3232

21 += .

The average energy of the oscillator in the given state is ______________ .

Q.51 A nucleus X undergoes a first forbidden -decay to a nucleus Y. If the angular momentum (I) and parity (P), denoted by I P as 7

2

for X, which of the following is a possible value for Y?

(A) 12

+

(B) 12

(C) 3

2

+

(D) 32

Q.52 The current gain of the transistor in the following circuit is = 100. The value of collector current Ic is _______________ mA.

Q.53 In order to measure a maximum of 1V with a resolution of 1mV using a n-bit A/D converter, working under the principle of ladder network, the minimum value of n is _____________ .

Q.54 If L+ and L are the angular momentum ladder operators, then, the expectation value of (+ + +), in the state | = 1, = 1 of an atom is ________ 2 .

Q.55 A low pass filter is formed by a resistance R and a capacitance C. At the cut-off angular frequency1

c RC =

, the voltage gain and the phase of the output voltage relative to the input voltage

respectively, are

(A) 0.71 and 450 (B) 0.71 and 450 (C) 0.5 and 900 (D) 0.5 and 900


Vo

Vi

20 F

20 F

12 V

3 k

3 k

150 k



GATE 2014 - Answer KeysGeneral Aptitude - GAQ. No. Key / Range Q. No. Key / Range Q. No. Key / Range1 A 5 1300 to 1300 9 D2 B 6 D 10 B3 D 7 B4 C 8 180 to 180

Physics - PHQ. No. Key / Range Q. No. Key / Range Q. No. Key / Range1 D 20 A 39 1.41 to 1.472 B 21 A 40 A3 A 22 B 41 B4 2.1 to 2.3 23 C 42 0.66 to 0.685 C 24 A 43 3.91 to 4.156 1.99 to 2.01 25 6.99 to 7.01 44 D7 1.49 to 1.51 26 A 45 10.58 to

10.708 D 27 D 46 C9 C 28 40 to 43 47 B10 D 29 A 48 C11 B 30 114 to 117 49 34.9 to 35.112 B 31 3.99 to 4.01 50 3.2 to 3.313 D 32 1.99 to 2.01 51 C14 0.99 to 1.01 33 D 52 1.4 to 1.715 1.99 to 2.01 34 B 53 9.99 to 10.0116 B 35 C 54 1.99 to 2.0117 D 36 2.3 to 2.4 55 B18 A 37 D19 C 38 0.24 to 0.26


Paper specific instructions:

1. There are a total of 65 questions carrying 100 marks.Questions are of multiple choice type or

numerical answer type. A multiple choice type question will have four choices for the answer with only one correct choice. For numerical answer type questions, the answer is a number and no choices will be given. A number as the answer should be entered using the virtual keyboard on the monitor.

2. Questions Q.1 Q.25 carry 1mark each. Questions Q.26 Q.55 carry 2marks each. The 2marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, then the answer to the second question in the pair will not be evaluated.

3. Questions Q.56 Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 Q.60 carry 1mark each, and questions Q.61 Q.65 carry 2marks each.

4. Questions not attempted will result in zero mark. Wrong answers for multiple choice type questions will result in NEGATIVE marks. For all 1 mark questions, mark will be deducted for each wrong answer. For all 2 marks questions, mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. There is no negative marking for questions of numerical answer type.

5. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall.

6. Do the rough work in the Scribble Pad provided.

PH: PHYSICS Duration: Three Hours Maximum Marks:100


GATE 2013 Solved Paper

Q. 1 Q. 25 carry one mark each. Q.1 f (x) is a symmetric periodic function of x i.e. f (x) = f (x). Then, in general, the Fourier series of

the function f(x) will be of the form

(A) cos sin (B) + cos (C) sin (D) + sin

Q.2 In the most general case, which one of the following quantities is NOT a second order tensor?

(A) Stress (B) Strain (C) Moment of inertia (D) Pressure

Q.3 An electron is moving with a velocity of 0.85c in the same direction as that of a moving photon.

The relative velocity of the electron with respect to photon is

(A) c (B) c (C) 0.15c (D) 0.15c Q.4 If Planck's constant were zero, then the total energy contained in a box filled with radiation of all

frequencies at temperature T would be ( k is the Boltzmann constant and T is nonzero)

(A) Zero (B) Infinite (C) (D)

Q.5 Across a first order phase transition, the free energy is

(A) proportional to the temperature (B) a discontinuous function of the temperature (C) a continuous function of the temperature but its first derivative is discontinuous (D) such that the first derivative with respect to temperature is continuous

Q.6 Two gases separated by an impermeable but movable partition are allowed to freely exchange

energy. At equilibrium, the two sides will have the same

(A) pressure and temperature (B) volume and temperature (C) pressure and volume (D) volume and energy

Q.7 The entropy function of a system is given by where and are positive

constants. The temperature of the system is

(A) negative for some energies (B) increases monotonically with energy (C) decreases monotonically with energy (D) Zero

Q.8 Consider a linear collection of N independent spin 1/2 particles, each at a fixed location. The

entropy of this system is (k is the Boltzmann constant)

(A) Zero (B) (C) (D) Q.9 The decay process violates

(A) baryon number (B) lepton number (C) isospin (D) strangeness



Q.10 The isospin (I) and baryon number (B) of the up quark is

(A) I=1, B=1 (B) I=1, B=1/3 (C) I=1/2, B=1 (D) I=1/2, B=1/3 Q.11 Consider the scattering of neutrons by protons at very low energy due to a nuclear potential of

range r0. Given that, cot where is the phase shift, k the wave number and the logarithmic derivative of the deuteron ground state wave function, the phase shift is

(A) (B) (C) (D) Q.12 In the decay process, the transition , is

(A) allowed both by Fermi and Gamow-Teller selection rule (B) allowed by Fermi and but not by Gamow-Teller selection rule (C) not allowed by Fermi but allowed by Gamow-Teller selection rule (D) not allowed both by Fermi and Gamow-Teller selection rule

Q.13 At a surface current, which one of the magnetostatic boundary condition is NOT CORRECT?

(A) Normal component of the magnetic field is continuous. (B) Normal component of the magnetic vector potential is continuous. (C) Tangential component of the magnetic vector potential is continuous. (D) Tangential component of the magnetic vector potential is not continuous.

Q.14 Interference fringes are seen at an observation plane z = 0, by the superposition of two plane waves . and . , where and are real amplitudes. The

condition for interference maximum is

(A) . (B) . (C) . (D) .

Q.15 For a scalar function satisfying the Laplace equation, has

(A) zero curl and non-zero divergence(B) non-zero curl and zero divergence (C) zero curl and zero divergence (D) non-zero curl and non-zero divergence

Q.16 A circularly polarized monochromatic plane wave is incident on a dielectric interface at Brewster

angle. Which one of the following statements is CORRECT ?

(A) The reflected light is plane polarized in the plane of incidence and the transmitted light is circularly polarized.

(B) The reflected light is plane polarized perpendicular to the plane of incidence and the transmitted light is plane polarized in the plane of incidence.

(C) The reflected light is plane polarized perpendicular to the plane of incidence and the transmitted light is elliptically polarized.

(D) There will be no reflected light and the transmitted light is circularly polarized.



Q.17 Which one of the following commutation relations is NOT CORRECT ? Here, symbols have their usual meanings.

(A) , (B) , (C) , (D) ,

Q.18 The Lagrangian of a system with one degree of freedom q is given by L = , where and are non-zero constants. If denotes the canonical momentum conjugate to q then which one of

the following statements is CORRECT?

(A) and it is a conserved quantity. (B) and it is not a conserved quantity. (C) and it is a conserved quantity. (D) and it is not a conserved quantity.

Q.19 What should be the clock frequency of a 6-bit A/D converter so that its maximum conversion time

is 32 s? (A) 1 MHz (B) 2 MHz (C) 0.5 MHz (D) 4 MHz

Q.20 A phosphorous doped silicon semiconductor ( doping density: 1017/cm3) is heated from 100C to

200C. Which one of the following statements is CORRECT ? (A) Position of Fermi level moves towards conduction band (B) Position of dopant level moves towards conduction band (C) Position of Fermi level moves towards middle of energy gap(D) Position of dopant level moves towards middle of energy gap

Q.21 Considering the BCS theory of superconductors, which one of the following statements is NOT

CORRECT? (h is the Planck's constant and e is the electronic charge)

(A) Presence of energy gap at temperatures below the critical temperature (B) Different critical temperatures for isotopes

(C) Quantization of magnetic flux in superconducting ring in the unit of (D) Presence of Meissner effect

Q.22 Group I contains elementary excitations in solids. Group II gives the associated fields with these

excitations. MATCH the excitations with their associated field and select your answer as per codes given below. Group I Group II (P) phonon (i) photon + lattice vibration (Q) plasmon (ii) electron + elastic deformation (R) polaron (iii) collective electron oscillations (S) polariton (iv) elastic wave Codes

(A) (P-iv), (Q-iii), (R-i), (S-ii) (B) (P-iv), (Q-iii), (R-ii), (S-i) (C) (P-i), (Q-iii), (R-ii), (S-iv) (D) (P-iii), (Q-iv), (R-ii), (S-i)

Q.23 The number of distinct ways of placing four indistinguishable balls into five distinguishable boxes

is ____________.



Q.24 A voltage regulator has ripple rejection of 50dB. If input ripple is 1 mV, what is the output ripple

voltage in V? The answer should be up to two decimal places. __________ Q.25 The number of spectral lines allowed in the spectrum for the transition in sodium is

____________.

Q. 26 to Q. 55 carry two marks each. Q.26 Which of the following pairs of the given function F(t) and its Laplace transform f (s) is NOT

CORRECT?

(A) F(t) = (t), f (s) = 1 , (Singularity at +0) (B) F(t) = 1, f (s) =

, (s > 0) (C) F(t) = sin kt, f (s) =

, (s > 0) (D) F(t) = t, f (s) = , (s > k, s > 0)

Q.27 If and are constant vectors, then is

(A) (B) (C) (D) Zero

Q.28 is equal to [Given (n+1) = n (n) and (1/2) = ] (A)

! (B) !! (C) !! (D) ! Q.29 The relativistic form of Newton's second law of motion is

(A) F =

(B) F =

(C) F =

(D) F = Q.30 Consider a gas of atoms obeying Maxwell-Boltzmann statistics. The average value of . over

all the momenta of each of the particles (where is a constant vector and is its magnitude, m is the mass of each atom, T is temperature and k is Boltzmann's constant) is,

(A) One (B) Zero (C) (D)

Q.31 The electromagnetic form factor F(q2) of a nucleus is given by,

where is a constant. Given that sin where (r) is the charge density, the root mean square radius of the nucleus is given by, (A) / (B) / (C) / (D) /



Q.32 A uniform circular disk of radius R and mass M is rotating with angular speed about an axis,

passing through its center and inclined at an angle 60 degrees with respect to its symmetry axis. The magnitude of the angular momentum of the disk is,

(A) (B) (C) (D)

Q.33 Consider two small blocks, each of mass M, attached to two identical springs. One of the springs is

attached to the wall, as shown in the figure. The spring constant of each spring is k. The masses slide along the surface and the friction is negligible. The frequency of one of the normal modes of the system is,

(A) (B) (C) (D) Q.34 A charge distribution has the charge density given by . For this

charge distribution the electric field at , , (A)

(B) (C) (D) Q.35 A monochromatic plane wave at oblique incidence undergoes reflection at a dielectric interface. If , and are the unit vectors in the directions of incident wave, reflected wave and the normal

to the surface respectively, which one of the following expressions is correct?

(A) (B) (C) (D)

Q.36 In a normal Zeeman effect experiment, spectral splitting of the line at the wavelength 643.8 nm

corresponding to the transition of cadmium atoms is to be observed. The spectrometer has a resolution of 0.01 nm. The minimum magnetic field needed to observe this is ( . , . , /) (A) 0.26 T (B) 0.52 T (C) 2.6 T (D) 5.2 T

Q.37 The spacing between vibrational energy levels in CO molecule is found to be 8.44x eV.

Given that the reduced mass of CO is 1.14x kg , Planck's constant is 6.626 Js and 1eV = 1.6x J. The force constant of the bond in CO molecule is (A) 1.87 N/m (B) 18.7 N/m (C) 187 N/m (D) 1870 N/m

Q.38 A lattice has the following primitive vectors (in ): , , .

The reciprocal lattice corresponding to the above lattice is

(A) BCC lattice with cube edge of 1 (B) BCC lattice with cube edge of 1 (C) FCC lattice with cube edge of 1 (D) FCC lattice with cube edge of 1

MM k k



Q.39 The total energy of an ionic solid is given by an expression where is Madelung

constant, r is the distance between the nearest neighbours in the crystal and B is a constant. If r0 is the equilibrium separation between the nearest neighbours then the value of B is

(A) (B) (C) (D)

Q.40 A proton is confined to a cubic box, whose sides have length m. What is the minimum

kinetic energy of the proton? The mass of proton is 1.67 kg and Planck's constant is 6.63 Js.

(A) 1.1 J (B) 3.3 J (C) 9.9 J (D) 6.6 J Q.41 For the function f (z)=

, the residue at the pole z = 1 is (your answer should be an integer) ___________.

Q.42 The degenerate eigenvalue of the matrix

is (your answer should be an integer) _________________ Q.43 Consider the decay of a pion into a muon and an anti-neutrino in the pion rest

frame. ./ , . / , The energy (in MeV) of the emitted neutrino, to the nearest integer is ____________

Q.44 In a constant magnetic field of 0.6 Tesla along the z direction, find the value of the path integral in the units of (Tesla m2) on a square loop of side length (1/ ) meters. The normal to the

loop makes an angle of 60 to the z-axis, as shown in the figure. The answer should be up to two decimal places. ____________

Q.45 A spin-half particle is in a linear superposition 0.8| + 0.6| of its spin-up and spin-down states. If

| and | are the eigenstates of then what is the expectation value, up to one decimal place, of the operator 10 + 5 ? Here, symbols have their usual meanings. ____________

Q.46 Consider the wave function (/r), where is the normalization constant. For r = 2, the

magnitude of probability current density up to two decimal places, in units of (/), is _____________.

60



Q.47 An n-channel junction field effect transistor has 5mA source to drain current at shorted gate (IDSS)

and 5V pinch off voltage (VP). Calculate the drain current in mA for a gate-source voltage (VGS) of 2.5V. The answer should be up to two decimal places. ________________

Common Data Questions Common Data for Questions 48 and 49: There are four energy levels E, 2E, 3E and 4E (where E >0). The canonical partition function of two particles is , if these particles are

Q.48 two identical fermions (A) (B) (C) (D)

Q.49 two distinguishable particles

(A) (B) (C) (D)

Common Data for Questions 50 and 51: To the given unperturbed Hamiltonian , we add a small perturbation given by ,

where is a small quantity.

Q.50 The ground state eigenvector of the unperturbed Hamiltonian is

(A) (1/,1/, ) (B) (1/, 1/, ) (C) (0,0,1) (D) (1,0,0)

Q.51 A pair of eigenvalues of the perturbed Hamiltonian, using first order perturbation theory, is

(A) 3+2, 7+2 (B) 3+2, 2+ (C) 3, 7+2 (D) 3, 2+2



Linked Answer Questions Statement for Linked Answer Questions 52 and 53: In the Schmidt model of nuclear magnetic moments, we have,

where the symbols have their usual meaning

Q.52 For the case /, where is the total angular momentum, the expectation value of in

the nuclear ground state is equal to,

(A) / (B) / (C) / (D) /

Q.53 For the O17 nucleus (A=17, Z=8), the effective magnetic moment is given by,

, where is equal to, ( . for proton and 3.83 for neutron) (A) 1.12 (B) 0.77 (C) 1.28 (D) 1.28

Statement for Linked Answer Questions 54 and 55: Consider the following circuit

Q.54 For this circuit the frequency above which the gain will decrease by 20 dB per decade is

(A) 15.9 kHz (B) 1.2 kHz (C) 5.6 kHz (D) 22.5 kHz

Q.55 At 1.2kHz the closed loop gain is

(A) 1 (B) 1.5 (C) 3 (D) 0.5

1k

2k

V(out)

1000pF

V(in)

10k



General Aptitude (GA) Questions Q. 56 Q. 60 carry one mark each. Q.56 A number is as much greater than 75 as it is smaller than 117. The number is:

(A) 91 (B) 93 (C) 89 (D) 96 Q.57 The professor ordered to the students to go out of the class.

I II III IV Which of the above underlined parts of the sentence is grammatically incorrect?

(A) I (B) II (C) III (D) IV Q.58 Which of the following options is the closest in meaning to the word given below:

Primeval

(A) Modern (B) Historic

(C) Primitive (D) Antique Q.59 Friendship, no matter how _________it is, has its limitations.

(A) cordial (B) intimate (C) secret (D) pleasant

Q.60 Select the pair that best expresses a relationship similar to that expressed in the pair:

Medicine: Health (A) Science: Experiment (B) Wealth: Peace (C) Education: Knowledge (D) Money: Happiness

Q. 61 to Q. 65 carry two marks each. Q.61 X and Y are two positive real numbers such that and . For which of the

following values of , the function , will give maximum value? (A) (4/3, 10/3) (B) (8/3, 20/3) (C) (8/3, 10/3) (D) (4/3, 20/3)

Q.62 If | | then the values of || | | is:

(A) 2, 1/3 (B) 1/2, 3 (C) 3/2, 9 (D) 2/3, 9



Q.63 Following table provides figures (in rupees) on annual expenditure of a firm for two years - 2010 and 2011.

Category 2010 2011 Raw material 5200 6240

Power & fuel 7000 9450

Salary & wages 9000 12600

Plant & machinery 20000 25000

Advertising 15000 19500

Research & Development 22000 26400 In 2011, which of the following two categories have registered increase by same percentage?

(A) Raw material and Salary & wages (B) Salary & wages and Advertising (C) Power & fuel and Advertising (D) Raw material and Research & Development

Q.64 A firm is selling its product at Rs. 60 per unit. The total cost of production is Rs. 100 and firm is

earning total profit of Rs. 500. Later, the total cost increased by 30%. By what percentage the price should be increased to maintained the same profit level.

(A) 5 (B) 10 (C) 15 (D) 30 Q.65 Abhishek is elder to Savar.

Savar is younger to Anshul. Which of the given conclusions is logically valid and is inferred from the above statements?

(A) Abhishek is elder to Anshul (B) Anshul is elder to Abhishek (C) Abhishek and Anshul are of the same age (D) No conclusion follows




GATE 2013 - Answer KeysPhysics - PHQ. No Key/Range Q. No Key/Range Q. No Key/Range1 B 23 70 45 7.62 D 24 3.16 46 0.253 B 25 3 47 1.254 B 26 C 48 B5 B 27 B 49 C6 A 28 C 50 C7 A 29 C 51 C8 D 30 C 52 B9 C 31 C 53 B10 D 32 C 54 A11 A 33 C 55 B12 C 34 A 56 D13 D 35 C 57 B14 B 36 B 58 C15 C 37 C 59 B16 C 38 A 60 C17 D 39 A 61 A18 D 40 C 62 B19 B 41 3 63 D20 C 42 5 64 A21 C 43 30 65 D22 B 44 0.15


PH : PHYSICS

Duration: Three Hours Maximum Marks: 100

Read the following instructions carefully.

1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator.

2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal and read the instructions printed on the ORS carefully.

3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble corresponding to your test paper code and the appropriate bubble under each digit of your registration number and (ii) write your registration number, your name and name of the examination centre and put your signature at the specified location.

4. This Question Booklet contains 20 pages including blank pages for rough work. After you are permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator.

5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each question has only one correct answer. Questions must be answered on the left hand side of the ORS by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen against the question number. For each question darken the bubble of the correct answer. More than one answer bubbled against a question will be treated as an incorrect response.

6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken the bubbles in the ORS very carefully.

7. Questions Q.1 Q.25 carry 1 mark each. Questions Q.26 Q.55 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then the answer to the second question in the pair will not be evaluated.

8. Questions Q.56 Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 Q.60 carry 1 mark each, and questions Q.61 Q.65 carry 2 marks each.

9. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks. For all 1 mark questions, mark will be deducted for each wrong answer. For all 2 marks questions, mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question.

10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.

11. Rough work can be done on the question paper itself. Blank pages are provided at the end of the question paper for rough work.

12. Before the start of the examination, write your name and registration number in the space provided below using a black ink ball point pen.

Name

Registration Number PH


GATE 2012 Solved Paper

Some Useful Constants

Speed of light in free space c = 3 108 m/s Boltzmann constant Bk = 1.380 1023 J/K Plancks constant h = 6.626 1034 J.s Electron charge e = 1.602 10-19 C Permittivity of free space 0 = 8.854 1012 C2/N.m2 Permeability of free space 0 = 4 107 H/m NOTE : In numerical problems, the option closest to the correct answer will be given credit.

Q. 1 Q. 25 carry one mark each. Q.1 Identify the CORRECT statement for the following vectors 3 2a i j and 2b i j

(A) The vectors a and b are linearly independent (B) The vectors a and b are linearly dependent (C) The vectors a and b are orthogonal (D) The vectors a and b are normalized

Q.2 Two uniform thin rods of equal length, L, and masses M1 and M2 are joined together along the length. The moment of inertia of the combined rod of length 2L about an axis passing through the mid-point and perpendicular to the length of the rod is,

(A) 21 2 12LM M (B) 21 2 6

LM M

(C) 21 2 3LM M (D) 21 2 2

LM M

Q.3 The space-time dependence of the electric field of a linearly polarized light in free space is given by 0 cos( )xE t kz where E0, and k are the amplitude, the angular frequency and the wavevector,

respectively. The time averaged energy density associated with the electric field is

(A) 20 014

E (B) 20 012 E (C) 2

0 0E (D) 20 02 E

Q.4 If the peak output voltage of a full wave rectifier is 10 V, its d.c. voltage is (A) 10.0 V (B) 7.07 V (C) 6.36 V (D) 3.18 V

Q.5 A particle of mass m is confined in a two dimensional square well potential of dimension a. This potential V(x,y) is given by ( , ) 0V x y for a x a and a y a elsewhere The energy of the first excited state for this particle is given by,

(A) 2 2

2ma

(B)

2 2

22ma

(C)

2 2

252ma

(D) 2 2

24ma



Q.6

The isothermal compressibility, of an ideal gas at temperature T0 and volume V0, is given by

(A) 00

1T

VV P

(B) 00

1T

VV P

(C)

0

0T

PVV

(D) 0

0T

PVV

Q.7 The ground state of sodium atom (11Na) is a 2S1/2 state. The difference in energy levels arising in the presence of a weak external magnetic field B, given in terms of Bohr magneton, B, is

(A) BB (B) 2BB (C) 4BB (D) 6BB

Q.8 For an ideal Fermi gas in three dimensions, the electron velocity vF at the Fermi surface is related to electron concentration n as,

(A) 2/3vF n (B) vF n (C) 1/2vF n (D) 1/3vF n

Q.9 Which one of the following sets corresponds to fundamental particles? (A) proton, electron and neutron (B) proton, electron and photon (C) electron, photon and neutrino (D) quark, electron and meson

Q.10 In case of a Geiger-Muller (GM) counter, which one of the following statements is CORRECT? (A) Multiplication factor of the detector is of the order of 1010 (B) Type of the particles detected can be identified (C) Energy of the particles detected can be distinguished (D) Operating voltage of the detector is few tens of Volts

Q.11 A plane electromagnetic wave traveling in free space is incident normally on a glass plate of refractive index 3/2. If there is no absorption by the glass, its reflectivity is

(A) 4% (B) 16% (C) 20% (D) 50%

Q.12 A Ge semiconductor is doped with acceptor impurity concentration of 1015 atoms/cm3. For the given hole mobility of 1800 cm2/V-s, the resistivity of this material is

(A) 0.288 cm (B) 0.694 cm (C) 3.472 cm (D) 6.944 cm

Q.13 A classical gas of molecules, each of mass m, is in thermal equilibrium at the absolute temperature, T. The velocity components of the molecules along the Cartesian axes are

,x yv v and zv . The mean value of 2x yv v is (A) Bk T

m (B) 3

2Bk Tm

(C) 12

Bk Tm

(D) 2 Bk Tm

Q.14 In a central force field, the trajectory of a particle of mass m and angular momentum L in plane polar coordinates is given by,

where, is the eccentricity of the particles motion. Which one of the following choices for gives rise to a parabolic trajectory?

(A) 0 (B) 1 (C) 0 1 (D) 1

21 1 cosmr L



Q.15

Identify the CORRECT energy band diagram for Silicon doped with Arsenic. Here CB, VB, ED and EF are conduction band, valence band, impurity level and Fermi level, respectively.

(A)

(B)

(C)

(D)

Q.16 The first Stokes line of a rotational Raman spectrum is observed at 12.96 cm-1. Considering the rigid rotor approximation, the rotational constant is given by

(A) 6.48 cm-1 (B) 3.24 cm-1 (C) 2.16 cm-1 (D) 1.62 cm-1

Q.17 The total energy, E of an ideal non-relativistic Fermi gas in three dimensions is given by 5

3

23

NEV

where N is the number of particles and V is the volume of the gas. Identify the CORRECT equation of state (P being the pressure),

(A) 13

PV E (B) 23

PV E (C) PV E (D) 53PV E

Q.18 Consider the wavefunction 1 2, sr r for a fermionic system consisting of two spin-half particles. The spatial part of the wavefunction is given by,

1 2 1 1 2 2 2 1 1 21, 2r r r r r r where 1 2and are single particle states. The spin part s of the wavefunction with spin states (+) and (-) should be

(A) 12

(B) 12

(C) (D)

Q.19 The electric and the magnetic fields ( , )E z t and ( , )B z t , respectively corresponding to the scalar potential (z,t) = 0 and vector potential ( , )A z t it z are (A) E iz and B jt (B) E iz and B jt (C) E iz and B jt (D) E iz and B jt

E D

C B

V B

EF

ED

C B

V B

EF

C B

V B

EF

E D

ED

C B

V B

E

EF



Q.20

Consider the following OP-AMP circuit.

Vin

+ 5 V

4 k1 k

+

+ 10 V

- 10 V

Vout

Which one of the following correctly represents the output Vout corresponding to the input Vin?

(A)

Vin

+ 5 V

Vout

- 10 V

+ 10 V

+ 1 V

t

t

0 V

(B)

Vin

+ 5 V

Vout

- 10 V

+ 10 V

+ 1 V

t

t

0 V

(C)

Vin

+ 5 V

Vout

- 10 V

+ 10 V

0 Vt

t

(D)

Vin

+ 5 V

Vout

- 10 V

+ 10 V

0 Vt

t

Q.21 Deuteron has only one bound state with spin parity 1+, isospin 0 and electric quadrupole moment 0.286 efm2. These data suggest that the nuclear forces are having (A) only spin and isospin dependence (B) no spin dependence and no tensor components (C) spin dependence but no tensor components (D) spin dependence along with tensor components



Q.22

A particle of unit mass moves along the x-axis under the influence of a potential, 2( ) 2V x x x . The particle is found to be in stable equilibrium at the point 2x . The time

period of oscillation of the particle is

(A) 2

(B) (C) 32

(D) 2

Q.23 Which one of the following CANNOT be explained by considering a harmonic approximation for the lattice vibrations in solids?

(A) Debyes 3T law (B) Dulong Petits law (C) Optical branches in lattices (D) Thermal expansion

Q.24 A particle is constrained to move in a truncated harmonic potential well (x > 0) as shown in the figure. Which one of the following statements is CORRECT?

(A) The parity of the first excited state is even (B) The parity of the ground state is even (C) The ground state energy is 1

2

(D) The first excited state energy is 72

Q.25 The number of independent components of the symmetric tensor Aij with indices i, j = 1, 2, 3 is

(A) 1 (B) 3 (C) 6 (D) 9

Q. 26 to Q. 55 carry two marks each.

Q.26 Consider a system in the unperturbed state described by the Hamiltonian, 01 00 1

H . The system

is subjected to a perturbation of the form H , where 1 . The energy eigenvalues of

the perturbed system using the first order perturbation approximation are

(A) 1 and (1+2) (B) (1+) and (1-) (C) (1+2) and (1-2) (D) (1+) and (1-2)

V(x)

x



Q.27

Inverse susceptibility (1/) as a function of temperature, T for a material undergoing paramagnetic to ferromagnetic transition is given in the figure, where O is the origin. The values of the Curie constant, C, and the Weiss molecular field constant, , in CGS units, are

(A) 5 25 10 , 3 10C (B) 2 53 10 , 5 10C (C) 2 43 10 , 2 10C (D) 4 22 10 , 3 10C

Q.28 A plane polarized electromagnetic wave in free space at time 0t is given by ( , ) 10 exp[ (6 8 )]E x z j i x z . The magnetic field ( , , )B x z t is given by

(A) 1( , , ) 6 8 exp[ (6 8 10 )]B x z t k i i x z ctc

(B) 1( , , ) 6 8 exp[ (6 8 10 )]B x z t k i i x z ct

c

(C) 1( , , ) 6 8 exp[ (6 8 )]B x z t k i i x z ctc

(D) 1( , , ) 6 8 exp[ (6 8 )]B x z t k i i x z ct

c

Q.29 The eigenvalues of the matrix 0 1 01 0 10 1 0

are

(A) 0, 1, 1

(B)

0, 2, 2 (C) 1 1, ,02 2 (D) 2, 2,0

Q.30

Match the typical spectroscopic regions specified in Group I with the corresponding type of transitions in Group II.

Group I Group II

(P) Infra-red region (i) electronic transitions involving valence electrons

(Q) Ultraviolet-visible region (ii) nuclear transitions

(R) X-ray region (iii) vibrational transitions of molecules

(S) -ray region (iv) transitions involving inner shell electrons (A) (P, i); (Q, iii); (R, ii); (S, iv) (B) (P, ii); (Q, iv); (R, i); (S, iii) (C) (P, iii); (Q, i); (R, iv); (S, ii) (D) (P, iv); (Q, i); (R, ii); (S, iii)

42 10

(CGS unit)

T

600 K 1

O



Q.31 In the following circuit, for the output voltage to be Vo = ( V1 + V2 /2), the ratio R1/R2 is

V2+

+ VCC

- VCC

Vo

R

RV1

R2

R1

(A) 1/2 (B) 1 (C) 2 (D) 3

Q.32 The terms 1 2j , j J arising from 2s13d1 electronic configuration in j-j coupling scheme are (A)

2,1 3,2

1 3 1 5, and ,

2 2 2 2 (B) 1,0 2,1

1 1 1 3, and ,

2 2 2 2

(C) 1,0 3,2

1 1 1 5, and ,

2 2 2 2 (D) 2,1 3,2

3 1 1 5, and ,

2 2 2 2

Q.33 In the following circuit, the voltage drop across the ideal diode in forward bias condition is 0.7 V.

24 Volt

12 k

6 k 3.3k

The current passing through the diode is

(A) 0.5 mA (B) 1.0 mA (C) 1.5 mA (D) 2.0 mA

Q.34 Choose the CORRECT statement from the following. (A) Neutron interacts through electromagnetic interaction (B) Electron does not interact through weak interaction (C) Neutrino interacts through weak and electromagnetic interaction (D) Quark interacts through strong interaction but not through weak interaction

Q.35 A rod of proper length l0 oriented parallel to the x-axis moves with speed 2c/3 along the x-axis in the S-frame, where c is the speed of the light in free space. The observer is also moving along the x-axis with speed c/2 with respect to the S-frame. The length of the rod as measured by the observer is

(A) 0.35 l0 (B) 0.48 l0 (C) 0.87 l0 (D) 0.97 l0

+

+ +



Q.36

A simple cubic crystal with lattice parameter ac undergoes transition into a tetragonal structure with lattice parameters at = bt = 2 ac and ct = 2ac, below a certain temperature. The ratio of the interplanar spacings of (1 0 1) planes for the cubic and the tetragonal structures is

(A) 16

(B) 16

(C) 38

(D) 38

Q.37 Consider the following circuit in which the current gain dc of the transistor is 100. + 15 V

900

100

100 k

Which one of the following correctly represents the load line (collector current IC with respect to collector-emitter voltage VCE) and Q-point of this circuit? (A)

Q-point(2 V, 13 mA)

15 mA

VCE 15 V

I C

(B)

Q-point(2 V, 10 mA)

13 mA

VCE 15 V

I C

(C)

Q-point(7.5 V, 7.5 mA)

15 mA

VCE 15 V

I C

(D)

Q-point(7.5 V, 6.5 mA)

13 mA

VCE 15 V

I C

Q.38 Consider a system whose three energy levels are given by 0, and 2. The energy level is two-fold degenerate and the other two are non-degenerate. The partition function of the system

with 1Bk T

is given by

(A) 1 2e (B) 22e e (C) 2(1 )e (D) 21 e e



Q.39

Two infinitely extended homogeneous isotropic dielectric media (medium-1 and medium-2 with dielectric constants 1

0

2 and 2

0

5 , respectively) meet at the z = 0 plane as shown in the figure. A uniform electric field exists everywhere. For z 0, the electric field is given by

1 2 3 5E i j k . The interface separating the two media is charge free.

The electric displacement vector in the medium-2 is given by

(A) 2 0[10 15 10 ]D i j k (B) 2 0[10 15 10 ]D i j k (C) 2 0[4 6 10 ]D i j k (D) 2 0[4 6 10 ]D i j k

Q.40 The ground state wavefunction for the hydrogen atom is given by 03/2

/100

0

1 14

r ae

a

,

where a0 is the Bohr radius.

The plot of the radial probability density, P(r) for the hydrogen atom in the ground state is (A)

(B)

(C)

(D)

Q.41 Total binding energies of O15, O16 and O17 are 111.96 MeV, 127.62 MeV and 131.76 MeV, respectively. The energy gap between 1p1/2 and 1d5/2 neutron shells for the nuclei whose mass number is close to 16, is

(A) 4.1 MeV (B) 11.5 MeV (C) 15.7 MeV (D) 19.8 MeV

z = 0

medium-1

medium-2



Q.42

A particle of mass m is attached to a fixed point O by a weightless inextensible string of length a. It is rotating under the gravity as shown in the figure. The Lagrangian of the particle is

2 2 2 21( , ) sin cos2L ma mga where and are the polar angles.

The Hamiltonian of the particle is

(A) 2

22 2

1cos

2 sinp

H p mgama

(B)

22

2 21

cos2 sin

pH p mga

ma

(C) 2 221 cos2H p p mgama (D) 2 221 cos2H p p mgama

Q.43 Given BrF , where kjiBB 0 is a constant vector and r is the position vector. The

value of C

rdF

, where C is a circle of unit radius centered at origin is,

(A) 0 (B) 02 B (C) 02 B (D) 1

Q.44 The value of the integral C

zdze1 , using the contour C of circle with unit radius 1z is

(A) 0 (B) 1-2 i (C) 1+2 i (D) 2 i

Q.45 A paramagnetic system consisting of N spin-half particles, is placed in an external magnetic field. It is found that N/2 spins are aligned parallel and the remaining N/2 spins are aligned antiparallel to the magnetic field. The statistical entropy of the system is,

(A) 2 ln 2BNk (B) ln 22 BN k

(C) 3 ln 22 BN k (D) ln 2BNk

C x

y

z

g

m

a



Q.46 The equilibrium vibration frequency for an oscillator is observed at 2990 cm-1. The ratio of the frequencies corresponding to the first and the fundamental spectral lines is 1.96. Considering the oscillator to be anharmonic, the anharmonicity constant is

(A) 0.005 (B) 0.02 (C) 0.05 (D) 0.1

Q.47 At a certain temperature T, the average speed of nitrogen molecules in air is found to be 400 m/s. The most probable and the root mean square speeds of the molecules are, respectively,

(A) 355 m/s, 434 m/s (B) 820 m/s, 917 m/s (C) 152 m/s, 301 m/s (D) 422 m/s, 600 m/s

Common Data Questions Common Data for Questions 48 and 49: The wavefunction of a particle moving in free space is given by, xkixki ee 2

Q.48 The energy of the particle is

(A) m

k2

5 22 (B)

m

k4

3 22

(C) m

k2

22 (D)

m

k 22

Q.49 The probability current density for the real part of the wavefunction is

(A) 1 (B) km

(C) 2

km

(D) 0

Common Data for Questions 50 and 51:

The dispersion relation for a one dimensional monatomic crystal with lattice spacing a , which interacts via nearest neighbour harmonic potential is given by

sin2

KaA , where A is a constant of appropriate unit.

Q.50 The group velocity at the boundary of the first Brillouin zone is

(A) 0 (B) 1 (C) 2

2Aa

(D) 21

2 2Aa

Q.51 The force constant between the nearest neighbour of the lattice is (M is the mass of the atom)

(A) 2

4MA

(B) 2

2MA

(C) 2MA

(D) 2 2MA



Linked Answer Questions Statement for Linked Answer Questions 52 and 53:

In a hydrogen atom, consider that the electronic charge is uniformly distributed in a spherical volume of radius a (= 0.5 10-10 m) around the proton. The atom is placed in a uniform electric field E = 30 105 V/m. Assume that the spherical distribution of the negative charge remains undistorted under the electric field.

Q.52 In the equilibrium condition, the separation between the positive and the negative charge centers is

(A) 8.66 10-16 m (B) 2.60 10-15 m (C) 2.60 10-16 m (D) 8.66 10-15 m

Q.53 The polarizability of the hydrogen atom in unit of (C2m/N) is (A) 2.0 10-40 (B) 1.4 10-41 (C) 1.4 10-40 (D) 2.0 10-39

Statement for Linked Answer Questions 54 and 55:

A particle of mass m slides under the gravity without friction along the parabolic path 2y ax as shown in the figure. Here a is a constant.

Q.54 The Lagrangian for this particle is given by,

(A) 2 212

L mx mgax (B) 2 2 2 21 (1 4 )2

L m a x x mgax

(C) 2 212

L mx mgax (D) 2 2 2 21 (1 4 )2

L m a x x mgax

Q.55 The Lagranges equation of motion of the particle is (A) 2x gax (B) 2 2 2 2(1 4 ) 2 4m a x x mgax ma xx (C) 2 2 2 2(1 4 ) 2 4m a x x mgax ma xx (D) 2x gax

y

x

m



General Aptitude (GA) Questions Q. 56 Q. 60 carry one mark each.

Q.56 Choose the grammatically INCORRECT sentence: (A) They gave us the money back less the service charges of Three Hundred rupees. (B) This countrys expenditure is not less than that of Bangladesh. (C) The committee initially asked for a funding of Fifty Lakh rupees, but later settled for a lesser

sum. (D) This countrys expenditure on educational reforms is very less.

Q.57 Which one of the following options is the closest in meaning to the word given below?

Mitigate (A) Diminish (B) Divulge (C) Dedicate (D) Denote

Q.58 Choose the most appropriate alternative from the options given below to complete the following sentence:

Despite several the mission succeeded in its attempt to resolve the conflict. (A) attempts (B) setbacks (C) meetings (D) delegations

Q.59 The cost function for a product in a firm is given by 5q2, where q is the amount of production. The firm can sell the product at a market price of 50 per unit. The number of units to be produced by the firm such that the profit is maximized is

(A) 5 (B) 10 (C) 15 (D) 25

Q.60 Choose the most appropriate alternative from the options given below to complete the following sentence:

Sureshs dog is the one was hurt in the stampede. (A) that (B) which (C) who (D) whom

Q. 61 - Q. 65 carry two marks each. Q.61 Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list R: Doubling each entry in a list doubles the mean of the list S: Doubling each entry in a list leaves the standard deviation of the list unchanged

(A) P, Q (B) Q, R (C) P, R (D) R, S



Q.62 An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of Xs shock absorbers, 96% are reliable. Of Ys shock absorbers, 72% are reliable.

The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is

(A) 0.288 (B) 0.334 (C) 0.667 (D) 0.720

Q.63 A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation y = 2x 0.1x2 where y is the height of the arch in meters. The maximum possible height of the arch is

(A) 8 meters (B) 10 meters (C) 12 meters (D) 14 meters

Q.64 Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal interviews to collect and collate economic data. Requirements: High School-pass, must be available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed.

Which one of the following is the best inference from the above advertisement?

(A) Gender-discriminatory (B) Xenophobic (C) Not designed to make the post attractive (D) Not gender-discriminatory

Q.65 Given the sequence of terms, AD CG FK JP, the next term is (A) OV (B) OW (C) PV (D) PW




GATE 2012 - Answer KeysPhysics - PHQ. No. Key / Range Q. No. Key / Range Q. No. Key / Range1 A 23 D 45 D2 C 24 D 46 B3 A 25 C 47 A4 C 26 A 48 C5 Marks to All 27 C 49 D6 A 28 A 50 A7 B 29 B 51 A8 D 30 C 52 C9 C 31 0 53 B10 A 32 A 54 B11 A 33 B 55 B12 C 34 A 56 D13 D 35 D 57 A14 B 36 C 58 B15 Marks to All 37 A 59 A16 C 38 C 60 Marks to All17 B 39 B 61 C18 B 40 D 62 B19 D 41 B 63 B20 A 42 B 64 D21 D 43 C 65 A22 B 44 D

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