deduction of ⅓ marks for a 1-mark question and ⅔ marks for a 2-mark question. 8. Non-programmable type Calculator is allowed

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1 . This question paper consists of sections, General Aptitude (GA) for 5 marks and the subject specific GATE paper for 85 marks. Both these sections are compulsory. The GA section consists of questions. Question numbers to 5 are of -mark each, while question numbers 6 to are of -mark each. The subject specific GATE paper section consists of 55 questions, out of which question numbers to 5 are of -mark each, while question numbers 6 to 65 are of -mark each.. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer type. 4. Multiple choice type questions will have four choices against (a),, (c), (d), out of which only ONE is the correct answer. 5. For numerical answer type questions, each question will have a numerical answer and there will not be any choices. 6. 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 ⅓ marks for a -mark question and ⅔ marks for a -mark question. 7. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE. 8. Non-programmable type Calculator is allowed -5, Mall Road, G.T.B. Nagar, Opp. G.T.B. Nagar Metro Station Gate No., Delhi- 9 Delhi- 6 DOWNLOAD CAREER ENDEAVOUR APP E : info@careerendeavour.com South Delhi : 8-A/, Jia Sarai, w : Near-IIT ww w.careerendeavour.com Hauz Khas, New Delhi-6, Ph : -6858, 6869 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

2 Q.-Q. 5 carry ONE mark each.. The digit in the unit position of the integer is x 4. If, then x 6 x 6 (a) x x (c) x 6 (d) x 6. In a flag, there are 5 paise coins, 5 paise coins and rupee coins, proportional to the numbers, 4 and. If the amount to Rs,, then number of rupee coins is (a) 4 5 (c) 8 (d) Choose the most appropriate word from the options given below to complete the following sentence. The official aswered that the complaints of the citizen would be looked into (a) respectably respectfully (c) reputably (d) respectively 5. Choose the statement where underlined word is used correctly (a) The minister insured the victims that everything would be all right He ensured that the company will not have to bear any loss (c) The actor got himself ensured against any accident (d) The teacher insured students of good result. Q.6-Q. carry TWO marks each. 6. The graph shows the production of rice in 6 states in 5, 6 and 7. What is the ratio of minimum production and maximum production in any of the given states in any of the given years? A B C D E F STATE (a) : : (c) : (d) : 4 7. If FRIEND is coded as HUMJTK, how is CANDLE written in that code? (a) EDRIRL DCQHQV (c) ESJFME (d) FYOBOC South Delhi : 8-A/, Jia Sarai, Near-IIT Hauz Khas, New Delhi-6, Ph : -6858, 6869 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

3 8. The word similar in meaning to dreary is (a) cheerful dreamy (c) hard (d) dismal 9. Fill in the blank with the correct idiom/phrase That boy from the town was a in the sleepy village (a) dog out of herd sheep from the heap (c) fish out of water (d) bird from the flock. Consider the statement Every house in every locality has atleast one member serving in either, Indian army or Indian airforce Negation of this statement is (a) There is a house in every locality that has no member serving in either Indian army or Indian airforce. There is a house in a locality that has all the members serving in either Indian army or Indian airforce. (c) There is a house in a locality that has no member serving in either Indian army or Indian airforce. (d) Every house in a locality has all the members serving in either Indian army or Indian airforce. Q.-Q.5 carry one mark each.. The average kinetic energy of an electron in the n = state of Li ++ is ev (upto one decimal places). A spin ½ particle is in a state where and are the eigenstates of S ˆz operator. The expectation value of the spin angular momentum measured along x-direction, is (a). The value of the commutator bracket xˆ (c) (d) ˆ 4, px (a) 4 i xˆ, pˆ x i xˆ, pˆ x (c) i xˆ, pˆ x (d) 4 ixˆ, pˆ x is 4. Let, m be the simultaneous eigenkets of ˆL and L ˆz respectively. The value of, Lˆ ˆ x ily, is (upto two decimal places) 5. An electron makes a transition from the valence band to the conduction band in a direct band gap semiconductor. Which of the following is not true? (a) there is momentum change in the electron a photon is absorbed in the process (c) electrons and hole pairs are created (d) the threshold of continuous optical absorption at frequency 6. An intrinsic material A has an energy gap.6 ev while material B has an energy gap of.7 ev. The ratio of intrinsic carriers densities n i i A n B at K is 7. The highest spin multiplicity of the spectroscopic terms resulting from the LS coupling of a p p 4d electrons. (a) (c) (d) 4 8. If the mass of the electron will be halved then ground state energy of the He + will (a) increase decrease (c) remain same (d) can t say South Delhi : 8-A/, Jia Sarai, Near-IIT Hauz Khas, New Delhi-6, Ph : -6858, 6869 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

4 9. The reduced mass of a molecule A is twice the reduced mass of a molecule B and also force constant of molecule A is twice the force constant of molecule B. Then the ratio of their ground state energy of pure vibrational motion is. If the reaction, p X proceeds via strong interaction, then the value of isospin I and its third component I of the particle X are respectively (a) and and (c) and (d) and. For the reaction, p k MeV MeV MeV, if m 6, m 98., 49.8 p m k c c and c m 9.5 MeV c MeV (upto two decimal places)., then the threshold kinetic energy of the pions when target proton is at rest is equal to. How many different output states the following circuit is having? S Q S Q S Q 4 CLK R Q R Q R Q (a) 4 (c) 5 (d) 6. In the transistor circuit shown in Figure, collector-to-ground voltage is + V. Which of the following is the probable cause of error? + V k + V 47 k (a) Collector-emitter terminals shorted (c) k resistor open Emitter to ground connection open (d) Collector-base terminals shorted 4. Which of the following cannot be Lagrangian of a particle where equation of motino is x x (a) x x (c) t t x x xx x x xe xe (d) x x xe t 5. A charged particle is placed in uniform electric field. The phase space trajectory of the particle is (a) straight line ellipse (c) parabola (d) hyperbola 6. Consider the following complex function, cot z f z z which of the following statements is/are CORRECT? (a) z n,,,... are simple poles of f(z) z= is a second order pole of f(z) (c) z = is a third order pole of f(z). (d) z = is removable singular point of f(z) South Delhi : 8-A/, Jia Sarai, Near-IIT Hauz Khas, New Delhi-6, Ph : -6858, 6869 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

5 7. The value of the integral 5 4 x e x dx is equal to (upto one decima; places) 8. A semicircular ring of radius R has uniform charge Q on its periphery. Its dipole moment with respect to origin at centre is (a) QR Q R (c) QR (d) 4 QR 9. Magnetic field in a region through which electromagnetic waves are propagating is given to be B B B ˆ cos kz cos tj. Average value of poynting vector is, then the value of k (an integer). A dielectric sphere of radius a and permitivity is surrounded by a dielectric shell of inner and outer radii a and b respectively. The potential inside the sphere and the shell are given respectively by ( r, ) Ar and ( r, ) Aa / r. The free charge density on the interface (a) zero ( ) A (c) ( ) A (d) A. A longwire carrying current I lies at rest in labframe in x-direction. An observer moves in x-direction with velocity v with respect to the wire. Charge density on wire measured by the observer will be Iv (a) c I c Iv (c) c v / c (d) Iv v / c. The heat of melting of ice at atmosphere pressure and ºC is.46 kcal/mol. The density of ice under these conditions is.97 g/cm and the density of water is.9998 g/cm. If mole of ice melted under these conditions, then the change in the internal energy will be (a).46 cal. cal (c). cal (d). cal. A system consists of N very weakly interacting particles at a temperature sufficiently high such that classical statistics are applicable. Each particle has mass m and oscillates in one direction about its equilibrium position. The heat capacity at temperature T,if restoring force is proportional to x. (a) Nk 5 Nk (c) Nk (d) Nk 4 4. Mass density of a circular disc of radius R and mass M is proportional to n th power of distance from center of 5 disc. If moment of inertia of disc about its axis passing through center and perpendicular to its plane lie 7 MR then value of n is (a) (c) `(d) 4 5. Let (p, q) and (P, Q) be two pairs of canonical variables. The transformation Q q cos p, P q sin p is canonical for (a),, (c), (d), c South Delhi : 8-A/, Jia Sarai, Near-IIT Hauz Khas, New Delhi-6, Ph : -6858, 6869 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

6 Q.6-Q.65 carry TWO marks each. 6. A particle of mass m is moving inside a deep square well potential, extending from x = to x = L. At time t =, the state vector of the particle is given as x x, t sin L L The uncertainty in the position of the particle, will be L. (Upto decimal places) 7. Consider the elastic scattering of 5 MeV neutrons from a nucleus. If the scattering is due to s wave and p wave only with phase shifts and respectively, then total cross-section will be barn. 6 (Upto decimal places). [Given : barn = 8 m ) V r, where is a positive constant. In a r stationary state, the relation between average kinetic energy and energy of the particle is 8. A particle is moving in a spherically symmetric potential (a) E E k Ek 5 E (c) Ek E (d) Ek E 9. A spherical blackbody A of radius cm, is maintained at a temperature of K. Another spherical blackbody B of radius 5 cm, is maintained at a temperature 4K. Let I and max denote the total intensity of radiation and the wavelength where maximum radiation is emitted. Then A (a) max B A B max, I A I B max max, I 6 A 9 I 5 A B A B 9 (c) max max, I A I B (d) max max, I A IB Consider a spinless particle of mass m, moving in an infinite potential well of length L, with walls at x = L and x = L V x L x L otherwise If the bottom of the potential, is modified by the perturbation V x V correction to ground state energy of the particle, is (a) 8V (c) V p B sin x L then first order 4. Which of the following is not true about BCS theory of superconductivity? (a) the electron-lattice-electron leads to an energy gap of observed magnitude an attractive interaction between electrons can lead to a ground state separated from excited state by an energy gap (c) magnetic flux through a superconductivity ring is quantised and effective unit of charge is e (d) the coherence length and penetration are not emerges as natural consequence of BCS theory. (d) V 6 South Delhi : 8-A/, Jia Sarai, Near-IIT Hauz Khas, New Delhi-6, Ph : -6858, 6869 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

7 4. The total resistivity of a sample can be written as the sum of contribution coming out from individual scattering process m ne impurity el el el phonon where, is the scattering rate. Which of the following is correct? (T = temperature) el el el phonon (a) goes as T while goes as T 5 el phonon impurity (c) goes as T (d) none of these goes as T while el el goes as T. 4. The debye temperature of carbon (diamond) is 8.5 K. The heighest lattice frequency involved in the debye theory is Hz (correct upto decimal places). 44. The magnetic moment of spectroscopic term p, in terms of Bohr s magneton is 45. A sodium atom in the first excited p states has a lifetime of 5 ns for decaying to the gro und s state. The corresponding line width of the transition (in frequency) units is (a). 7 Hz. 7 Hz (c) 4 6 Hz (d).5 7 Hz 46. The strangeneous and hypercharge of a neutral elementary particle which has baryon number B = + and third component of Isospin I = ½ are, respectively (a) and and (c) and (d) and X7 and Y 7 are mirror nuclei. If their coulomb energy difference is MeV, then their radius is equal to fermi. (upto two decimal places) V 48. A diode whose terminal characteristic are related as I D I s, where I s is the reverse saturation current VT and V T is the thermal voltage (= 5 mv), is based at ID ma. Its dynamic resistance is ohms (an integer). 49. For the diode circuit shown, VZ ON is V i 6 V, V of diodes to be.7 V the required value of V i to get zener diode k D k V 6V V 7 (a).7 Vi 6V Vi 6V (c).7 Vi 8.V (d) Vi 8.V 5. For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are ns,.5 ns and ns, respectively. If all the inputs P, Q, R, S and T are applied at the same time instant, the maximum propagation delay (in ns) of the circuit is P Q R S MUX S MUX S Y T South Delhi : 8-A/, Jia Sarai, Near-IIT Hauz Khas, New Delhi-6, Ph : -6858, 6869 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

8 5. A solid sphere of mass M and radius R rolls down an inclined plane of inclination, from a height h. If the sphere starts from rest then work done by frictional torque on the sphere during the time it take to reach bottom of inclined plane is (a) mgh sin 5 mgh (c) 7 mgh (d) 5 7 mgh 5. Two particle each of rest mass m are moving in +x and +y direction with equal speed c/ with respect to lab frame. The energy of one particle in rest frame of the other is (a) m c 4 m c (c) m c (d) m c 5. The alzebraic multiplicity of the eigenvalue, corresponding to the following matrix 4 is equal to (an integer) 54. The fourier transform of the function, 5 8 ikx F f x f x e dx f x e a xb (a, b are positive real constant) will be ikb a ikb a kb a (a) e e (c) e k a k a k a kb a (d) e k a 55. Consider the following function, If f f x (where for x for x x is represented by the following series, f x CP x CP x... CnPn x... Pn x is Legendre polynomial of order n), then the value of the coefficient C will be equal to (upto two decimal places) 56. Which of the following relation is/are not CORRECT? (Symbols have their usual meanings) (a) Lˆ, ˆ ˆ i L j i ijk Lk ˆi, ˆ j i ijk k South Delhi : 8-A/, Jia Sarai, Near-IIT Hauz Khas, New Delhi-6, Ph : -6858, 6869 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

9 (c) ˆ ˆ i ˆ (d) ijk i j k i j ijk k A B C A B C A long wire lying in z-direction carries a time varying current. At some point (x, y, z) near the middle of wire which of the following is true for electric field (a) E E E E E, E x y z x y z (c) E E, E (d) E, E, E x y z x y z 58. A circular wire of radius R carries a current I I cost. Magnetic field at the distance r from centre of wire c for r >> R and r n varies as B kr. The value of n is (an integer) 59. When relativistic charge particle is thrown into perpendicular magnetic field. It moves in circular path. If radius of circular orbits be R and R for kinetic energies m c and m c respectively then value of 6. A carnot engine has a cycle as shown in the figure below. If W and W ' represents work done by mole of monatomic and diatomic gas, respectively, then the ratio (Your answer should be upto two decimal places) P 4T W ' W R R is 4 T V 64V 6. A ohm resistor is held at a constant temperature of K. A current of amperes is passed through the resistor for sec. The change in entropy of the resistor is (J/K) 6. The relative energy fluctuation E of an ideal gas of N atoms at temperature T is : E (a) / N N / (c) N (d) 6. Consider a system of two atoms, each having only quantum states of energies, and. The system is in contact with a heat reservoir at temperature T. Assume the particles obey classical statistics and are indistinguishable The partition function of the system will be V N (a) exp exp exp exp (c) exp exp exp (d) exp exp exp South Delhi : 8-A/, Jia Sarai, Near-IIT Hauz Khas, New Delhi-6, Ph : -6858, 6869 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

10 64. The Lagrangian of a diatomic molecule is given by m k L x x x x where, m is the mass each atom and x, x are displacements from equilibrium position and k >. The normal frequencies are (a) k m / k m /4 (c) k m /4 (d) k m / p 65. The Hamiltonian of a particle is H pq, where q is generalised coordinate and p is the corresponding canonical momentum. The Lagrangian m is (a) m dq q dt m dq q dt (c) m dq dq q q dt dt (d) m dq dq q q dt dt South Delhi : 8-A/, Jia Sarai, Near-IIT Hauz Khas, New Delhi-6, Ph : -6858, 6869 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

11 Space for rough work South Delhi : 8-A/, Jia Sarai, Near-IIT Hauz Khas, New Delhi-6, Ph : -6858, 6869 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

12 PHYSICS-PH GATE TEST SERIES-D Date: 4--8 ANSWER KEY. (). (d) (a) 7. (a) 8. (d) 9. (d). (c). (.5 to.7).. (d) 4. (.4 to.48) 5. (a) 6. ( to ) 7. (d) 8. (a) 9. (). (a). (899 to 89). (d). 4. (d) 5. (c) 6. (c) 7. (.5) 8. (a) 9. (). (c). (c).. (d) 4. (c) 5. (d) 6. (.6 to.9) 7. (.7 to.9) 8. (a) 9. (a) 4. (a) 4. (d) 4. (a) 4. (.86) 44. (.64 to.69) 45. (a) 46. (d) 47. (7.75 to 7.79) 48. (.4 to.7) 49. (d) 5. (7) 5. (c) () () 56. (c) ( ) 59. (.6 to.65) 6. (. to.4) 6. () 6. (a) (d) 65. South Delhi : 8-A/, Jia Sarai, Near-IIT Hauz Khas, New Delhi-6, Ph : -6858, 6869 North Delhi : -5, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. ), Delhi-9, Ph: ,

deduction of ⅓ marks for a 1-mark question and ⅔ marks for a 2-mark question. 8. Non-programmable type Calculator is allowed

deduction of ⅓ marks for a 1-mark question and ⅔ marks for a 2-mark question. 8. Non-programmable type Calculator is allowed . This question paper consists of sections, General Aptitude (GA) for 5 marks and the subject specific GATE paper for 85 marks. oth these sections are compulsory. The GA section consists of 0 questions.