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GATE 2014 : Physics

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GATE 2014 Examination PH: Physics 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 SET- 1 General Aptitude -GA 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 Q.2 (B) meaning (C) concentration (D) stability Choose the most appropriate word from the options given below to complete the following sentence. One of his biggest ______ was his ability to forgive. Q.3 (B) virtues (C) choices (D) strength 20 14 (A) vice 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 Rajan s 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 (C) is parallel to the x-axis E 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? G AT Q.5 (B) has a slope of +1 (D) has a slope of 1 Q. 6 Q. 10 carry two marks each. Q.6 Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK (A) ALRVX Q.7 (C) ITZDF (D) OYEIK 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 Faisal s 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? (A) (B) (C) (D) GA (B) EPVZB Anuj 6 2 4 2 Bhola 2 6 2 4 Chandan 5 5 6 6 Dilip 1 1 3 1 Eswar 3 3 1 3 Faisal 4 4 5 5 1/2 GATE 2014 SET- 1 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 (C) 1.5 (D) 1.25 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) E 20 14 Q.10 (B) 2.5 G AT (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) (C) (ii) and (iii) (B) (i) and (iii) (D) (iii) and (iv) END OF THE QUESTION PAPER GA 2/2 GATE 2014 SET 1 PHYSICS-PH Some Useful Constants = 3 108 / = 1.380 10 23 / = 6.626 10 34 . = 1.602 10 19 0 = 8.854 10 12 2 / . 2 0 = 4 10 7 / me = 9.31 10-31 kg m p = 1.67 10 27 kg Mass of neutron mn = 1.675 10-27 kg PH (G AT E 20 14 ) Speed of light in free space Boltzmann constant Planck s constant Electron charge Permittivity of free space Permeability of free space Mass of electron Mass of proton PH 1/1 GATE 2014 SET 1 PHYSICS-PH Q. 1 Q. 25 carry one mark each. The unit vector perpendicular to the surface x 2 + y 2 + z 2 = 3 at the point (1,1,1) is (A) Q.2 + y z x 3 (B) (B) Charge Q.5 y +z x 3 + y +z x (D) 3 (C) Current (D) Electric field The number of normal Zeeman splitting components of 1P 1D transition is (A) 3 Q.4 (C) Which one of the following quantities is invariant under Lorentz transformation? (A) Charge density Q.3 y z x 3 (B) 4 (C) 8 (D) 9 20 14 ) Q.1 If the half-life of an elementary particle moving with speed 0.9c in the laboratory frame is 5 10 8 s, then the proper half-life is __________ 10-8 s. ( = 3 108 / ) 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) 0 0 (B) 45 0 (C) 90 0 (D) 120 0 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, E Q.6 10 cos 6 10 7 t 0.4 z V/m. E=x AT ( ) 8 The phase velocity of the wave is ________________ 10 m/s. The matrix A= 1 1 1 + i 3 1 i 1 (G Q.8 PH (A) orthogonal Q.9 is (B) symmetric (C) anti-symmetric (D) unitary The recoil momentum of an atom is p A when it emits an infrared photon of wavelength 1500 nm, and it is p B when it emits a photon of visible wavelength 500 nm. The ratio (A) 1 : 1 Q.10 (C) 1 : 3 (B) V 2 / 3 (C) V 3 / 5 (D) V 5 / 3 Which one of the following high energy processes is allowed by conservation laws? (A) p + p 0 + 0 (B) + p 0 + n (C) n p + e + e PH (D) 3 : 2 For a gas under isothermal conditions, its pressure P varies with volume V as P V 5 / 3 . The bulk modulus B is proportional to (A) V 1/ 2 Q.11 (B) 1 : 3 pA is pB (D) + e + + 1/10 GATE 2014 Q.12 SET 1 PHYSICS-PH ( ) + (dx ) The length element ds of an arc is given by, (ds ) 2 = 2 dx1 2 2 2 + 3 dx1dx 2 .The metric tensor g ij is 3 2 3 2 (C) 3 2 1 3 2 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) (C) Q.14 1 3 2 3 2 1 3 2 2 2 1 2 1 2 [ 1 ( x1 ) 2 ( x1 ) 1 ( x2 ) 2 ( x2 )] [ 1 ( x1 ) 2 ( x1 ) + 1 ( x2 ) 2 ( x2 )] If the vector potential (B) (D) 1 2 1 2 [ 1 ( x1 ) 2 ( x2 ) + 1 ( x2 ) 2 ( x1 )] [ 1 ( x1 ) 2 ( x2 ) 1 ( x2 ) 2 ( x1 )] E Q.13 (B) (D) 3 1 20 14 ) 2 (A) + 2y y 3z z , A= xx AT satisfies the Coulomb gauge, the value of the constant is ___________________ . 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? (G Q.15 (A) particle (C) Hydrogen atom (D) Deuteron 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. PH Q.17 (B) 4Be7 nucleus (A) X ++ (B) X + (C) X (D) X Q.18 The Hamilton s canonical equations of motion in terms of Poisson Brackets are Q.19 (A) = { , } ; (B) = { , } ; (C) = { , } ; (D) = { , } ; The Miller indices of a plane passing through the three points having coordinates (0,0,1), 1 1 1 (1,0,0), , , are 2 2 4 (A) (212) PH = { , } = { , } = { , } = { , } (B) (111) (C) (121) (D) (211) 2/10 GATE 2014 Q.20 SET 1 PHYSICS-PH The plot of specific heat versus temperature across the superconducting transition temperature ( ) is most appropriately represented by (A) (B) Cp Cp (C) (D) T Cp Cp T T is the spin angular momentum, then does NOT If is the orbital angular momentum and . commute with (B) 2 (C) 2 2 + (D) PH (G AT (A) E Q.21 T 20 14 ) PH 3/10 GATE 2014 Q.22 SET 1 PHYSICS-PH 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) /a O - /a The variation of the group velocity is most appropriately represented by /a O (C) - /a (D) O /a k - /a /a k O /a k (G 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) PH N(E) N(E) E (C) E (D) N(E) N(E) E PH O AT - /a k E - /a Q.23 (B) 20 14 ) (A) E 4/10 GATE 2014 Q.24 SET 1 PHYSICS-PH The input given to an ideal OP-AMP integrator circuit is V V0 t t0 The correct output of the integrator circuit is (A) (B) V V V0 t t0 t t0 (C) (D) V V V0 V0 t t0 t E t0 The minimum number of flip-flops required to construct a mod-75 counter is _______. PH (G AT Q.25 20 14 ) V0 PH 5/10 GATE 2014 SET 1 PHYSICS-PH 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 m (A) mr Q.27 (B) r 20 14 ) 450 1 mr 2 (C) 1 mr 2 (D) 2mr An electron in the ground state of the hydrogen atom has the wave function 1 ( ) = 0 3 0 = z 2 r 2 , where z = r cos is where 0 is constant. The expectation value of the operator Q ( ) +1 = ( 1)! +1 ) E (Hint: = 0 2 (B) 0 2 (C) 3 0 /2 Q.29 A particle of mass m is in a potential given by AT Q.28 2 (A) 0 /2 2 (D) 2 0 (G 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 10 21 2 ) a ar 2 V (r ) = + 03 , r 3r PH 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) 2 Q.30 Q.31 PH mr03 2a (B) 2 mr03 a (C) 2 2mr03 a (D) 4 mr03 a 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 ) A particle of mass is subjected to a potential, 1 ( , ) = 2 ( 2 + 2 ), , 2 The state with energy 4 is -fold degenerate. The value of is ___________ . 6/10 GATE 2014 Q.32 SET 1 PHYSICS-PH A hydrogen atom is in the state 8 3 4 = 21 200 7 310 + 21 321 , 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) 2r0 km Q.34 2r0 km (C) r0 km (D) r0 km 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 Q.35 (B) (B) JA = 3, JB = 1 The value of the integral 20 14 ) Q.33 where , , in denote the principal, orbital and magnetic quantum numbers, respectively. If 2 is the angular momentum operator, the average value of 2 is ______________ . (C) JA = 5, JB = 0 (D) JA = 6, JB = 1 z2 e z + 1 dz , C where C is the circle z = 4 , is (C) 4 3 i (D) 4 2 i 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 P ( r0 , / 4 ) in plane polar coordinates is r 3e , where e r and e are the unit vectors. The emerging ray in Region 2 has the E1 = 7e electric field E2 parallel to x- axis. If 1 and 2 are the dielectric constants of Region 1 and AT Q.36 (B) 2 2 i E (A) 2 i 2 is ____________________________ 1 PH (G Region 2 respectively, then PH 7/10 GATE 2014 Q.37 SET 1 PHYSICS-PH The solution of the differential equation d2y y = 0, d t2 subject to the boundary conditions y (0 ) = 1 and y ( ) = 0 , is (A) cos t + sin t (B) cosh t + sinh t (C) cos t - sin t (D) cosh t - sinh t 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: m p = 1.67 10 27 kg, = 1.6 10 19 ) Q.40 20 14 ) Q.38 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 = Q.42 (B) 2 1 + 2e +e 2 e + e 2 2 + e + e 2 (D) 1 + e 2e + e 2 e + 2 e 2 2 + e + e 2 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 (G Q.41 E (C) e + 2 e 2 AT (A) 1 is given by k BT 1 and 2 are two orthogonal states of a spin 1 system. It is given that 1 = 2 0 1 1 + , 3 3 0 1 0 PH 1 2 where 0 and 1 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 PH 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 10 34 . ) 8/10 GATE 2014 Q.44 SET 1 PHYSICS-PH The Hamiltonian of a particle of mass m is given by H = p2 q2 . Which one of the following 2m 2 figures describes the motion of the particle in phase space? (C) E 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 10 12 2 / . 2 ) AT Q.46 (D) 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 10 34 . , = 3 108 / , = 1.380 10 23 / ) (G Q.45 (B) 20 14 ) (A) (A) 2.03 10-5 Q.48 (C) 7.02 10-5 (D) 9.83 10-5 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 PH Q.47 (B) 4.02 10-5 (A) ln2 (B) 2 ln2 (C) 2 ln4 (D) 3 ln4 A particle is confined to a one dimensional potential box with the potential V (x ) = 0, 0 < x < a = , otherwise If the particle is subjected to a perturbation, within the box, W = x , where is a small constant, the first order correction to the ground state energy is (A) 0 Q.49 PH (B) a / 4 (C) a / 2 (D) a Consider the process + + + + . The minimum kinetic energy of the muons ( ) in the centre of mass frame required to produce the pion ( ) pairs at rest is __________ MeV. (Given: m = 105 MeV/c2, m = 140 MeV/c2). 9/10 GATE 2014 Q.50 SET 1 PHYSICS-PH A one dimensional harmonic oscillator is in the superposition of number states, n , given by = 1 3 2 + 3 . 2 2 The average energy of the oscillator in the given state is ______________ . A nucleus X undergoes a first forbidden -decay to a nucleus Y. If the angular momentum (I) and 7 parity (P), denoted by I P as for X, which of the following is a possible value for Y? 1+ Q.52 (B) (A) 2 2 1 2 (C) 3+ 2 (D) 3 2 The current gain of the transistor in the following circuit is = 100. The value of collector current Ic is _______________ mA. 12 V 20 14 ) Q.51 3 k 20 F Vo 150 k 20 F E Vi AT 3 k 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 . A low pass filter is formed by a resistance R and a capacitance C. At the cut-off angular frequency PH Q.55 (G Q.53 c = 1 , the voltage gain and the phase of the output voltage relative to the input voltage RC respectively, are (A) 0.71 and 450 (B) 0.71 and 450 (C) 0.5 and 900 (D) 0.5 and 900 END OF THE QUESTION PAPER PH 10/10

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