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GATE 2016 : Physics

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GATE 2016 General Aptitude - GA Set-2 Q. 1 Q. 5 carry one mark each. Q.1 The volume of a sphere of diameter 1 unit is ________ than the volume of a cube of side 1 unit. (A) least Q.2 (B) less (B) hanging (C) hankering (D) hung Choose the statement(s) where the underlined word is used correctly: (i) (ii) (iii) A prone is a dried plum. He was lying prone on the floor. People who eat a lot of fat are prone to heart disease. (A) (i) and (iii) only Q.4 (D) low The unruly crowd demanded that the accused be _____________ without trial. (A) hanged Q.3 (C) lesser (B) (iii) only (C) (i) and (ii) only (D) (ii) and (iii) only Fact: If it rains, then the field is wet. Read the following statements: (i) It rains (ii) The field is not wet (iii) The field is wet (iv) It did not rain Which one of the options given below is NOT logically possible, based on the given fact? (A) If (iii), then (iv). (C) If (i), then (ii). Q.5 (B) If (i), then (iii). (D) If (ii), then (iv). A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6 m, the area of the window in m2 is ___________. (A) 1.43 (B) 2.06 (C) 2.68 (D) 2.88 1/3 GATE 2016 General Aptitude - GA Set-2 Q. 6 Q. 10 carry two marks each. Q.6 Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group Q was 5. Assuming that the marks were distributed on a normal distribution, which of the following statements will have the highest probability of being TRUE? (A) No student in group Q scored less marks than any student in group P. (B) No student in group P scored less marks than any student in group Q. (C) Most students of group Q scored marks in a narrower range than students in group P. (D) The median of the marks of group P is 100. Q.7 A smart city integrates all modes of transport, uses clean energy and promotes sustainable use of resources. It also uses technology to ensure safety and security of the city, something which critics argue, will lead to a surveillance state. Which of the following can be logically inferred from the above paragraph? (i) (ii) (iii) (iv) All smart cities encourage the formation of surveillance states. Surveillance is an integral part of a smart city. Sustainability and surveillance go hand in hand in a smart city. There is a perception that smart cities promote surveillance. (A) (i) and (iv) only (C) (iv) only Q.8 (B) (ii) and (iii) only (D) (i) only Find the missing sequence in the letter series. B, FH, LNP, _ _ _ _. (A) SUWY Q.9 (B) TUVW (C) TVXZ (D) TWXZ The binary operation is defined as a b = ab+(a+b), where a and b are any two real numbers. The value of the identity element of this operation, defined as the number x such that a x = a, for any a, is . (A) 0 (B) 1 (C) 2 (D) 10 2/3 GATE 2016 Q.10 General Aptitude - GA Set-2 Which of the following curves represents the function ln Here, represents the abscissa and represents the ordinate. for ? (A) (B) (C) (D) END OF THE QUESTION PAPER 3/3 GATE 2016 Physics Q. 1 Q. 25 carry one mark each. Q.1 Consider the linear differential equation dy xy. If y 2 at x 0, then the value of y at x=2 is dx given by (A) e 2 (C) e 2 Q.2 (B) 2e 2 (D) 2e 2 ? Which of the following magnetic vector potentials gives rise to a uniform magnetic field B 0 k (A) B0 z k (C) Q.3 B0 x yi j 2 (B) B0 x j (D) B0 yi x j 2 17 The molecule O2 is (A) Raman active but not NMR (nuclear magnetic resonance) active. (B) Infrared active and Raman active but not NMR active. (C) Raman active and NMR active. (D) Only NMR active. Q.4 There are four electrons in the 3d shell of an isolated atom. The total magnetic moment of the atom in units of Bohr magneton is ________. Q.5 Which of the following transitions is NOT allowed in the case of an atom, according to the electric dipole radiation selection rule? (A) 2s-1s Q.6 PH (D) 3d-2p has Isospin = 0 , Strangeness = 0 Isospin = 1 , Strangeness = 0 Isospin = 1/2, Strangeness = +1 Isospin = 1/2, Strangeness = -1 The magnitude of the magnetic dipole moment associated with a square shaped loop carrying a steady current I is m. If this loop is changed to a circular shape with the same current I passing through it, the magnetic dipole moment becomes Q.8 (C) 2p-2s In the SU(3) quark model, the triplet of mesons , 0 , (A) (B) (C) (D) Q.7 (B) 2p-1s pm . The value of p is ______. The total power emitted by a spherical black body of radius R at a temperature T is P1. Let P2 be the total power emitted by another spherical black body of radius R/2 kept at temperature 2T. The ratio, P1/P2 is _______. (Give your answer upto two decimal places) 1/10 GATE 2016 Physics Q.17 The kinetic energy of a particle of rest mass m0 is equal to its rest mass energy. Its momentum in units of m 0 c , where c is the speed of light in vacuum, is _______. (Give your answer upto two decimal places) Q.18 The number density of electrons in the conduction band of a semiconductor at a given temperature is 2 1019 m 3 . Upon lightly doping this semiconductor with donor impurities, the number density of conduction electrons at the same temperature becomes 4 10 20 m 3 . The ratio of majority to minority charge carrier concentration is ________. Q.19 Two blocks are connected by a spring of spring constant k . One block has mass m and the other block has mass 2m. If the ratio k/m = 4 s 2 , the angular frequency of vibration of the two block spring system in s 1 is _______. (Give your answer upto two decimal places) Q.20 A particle moving under the influence of a central force F (r ) k r (where r is the position vector of the particle and k is a positive constant) has non-zero angular momentum. Which of the following curves is a possible orbit for this particle? (A) (B) (C) (D) Q.21 Q.22 A straight line segment passing through the origin. An ellipse with its center at the origin. An ellipse with one of the foci at the origin. A parabola with its vertex at the origin. Consider the reaction (A) 54 25 Mn + e (B) e 54 24 Cr + X . The particle X is (C) n (D) 0 The scattering of particles by a potential can be analyzed by Born approximation. In particular, if the scattered wave is replaced by an appropriate plane wave, the corresponding Born approximation is known as the first Born approximation. Such an approximation is valid for (A) large incident energies and weak scattering potentials. (B) large incident energies and strong scattering potentials. (C) small incident energies and weak scattering potentials. (D) small incident energies and strong scattering potentials. Q.23 Consider an elastic scattering of particles in l 0 states. If the corresponding phase shift 0 is 90 0 and the magnitude of the incident wave vector is equal to 2 2 fm-1 then the total scattering cross section in units of fm is _______. Q.24 , the A hydrogen atom is in its ground state. In the presence of a uniform electric field E E0 z n leading order change in its energy is proportional to ( E0 ) . The value of the exponent n is _______. PH 3/10 GATE 2016 Physics Q.25 A solid material is found to have a temperature independent magnetic susceptibility, C . Which of the following statements is correct? (A) If C is positive, the material is a diamagnet. (B) If C is positive, the material is a ferromagnet. (C) If C is negative, the material could be a type I superconductor. (D) If C is positive, the material could be a type I superconductor. Q. 26 Q. 55 carry two marks each. Q.26 An infinite, conducting slab kept in a horizontal plane carries a uniform charge density . Another infinite slab of thickness t, made of a linear dielectric material of dielectric constant k, is kept above the conducting slab. The bound charge density on the upper surface of the dielectric slab is 2k ( k 2) (C) 2k k ( k 1) (D) k (B) (A) Q.27 The number of spectroscopic terms resulting from the L S coupling of a 3p electron and a 3d electron is _______. Q.28 Which of the following statements is NOT correct? (A) A deuteron can be disintegrated by irradiating it with gamma rays of energy 4 MeV. (B) A deuteron has no excited states. (C) A deuteron has no electric quadrupole moment. (D) The 1S0 state of deuteron cannot be formed. Q.29 If s1 and s 2 are the spin operators of the two electrons of a He atom, the value of s1 s 2 for the ground state is (A) Q.30 3 2 2 (B) 3 2 4 (C) 0 (D) 1 2 4 2 2 is 2mL2 A two-dimensional square rigid box of side L contains six non-interacting electrons at T = 0 K. The mass of the electron is m. The ground state energy of the system of electrons, in units of _______. Q.31 An alpha particle is accelerated in a cyclotron. It leaves the cyclotron with a kinetic energy of 16 MeV. The potential difference between the D electrodes is 50 kilovolts. The number of revolutions the alpha particle makes in its spiral path before it leaves the cyclotron is ______. Q.32 Let be the expression for (A) j kVi PH component of a vector field is equal to (B) j k Vi , which has zero divergence. If 2 (C) j Vi / , the 2 (D) j Vi 4/10 GATE 2016 Physics Q.33 (A) Q.34 j 2k The direction of j 2k for a scalar field ( , , ) = 5 (B) 5 (C) j 2k + j 2k at the point (1,1,2) is (D) 5 5 x , y and z are the Pauli matrices. The expression 2 x y y x is equal to (A) 3i z (B) i z (C) i z (D) 3i z Q.35 A particle of mass = 0.1 kg is initially at rest at origin. It starts moving with a uniform = 0. The action of the particle, in units of J-s, at = 2 is acceleration a 10 i ms 2 at ______. (Give your answer upto two decimal places) Q.36 A periodic function ( ) of period 2 is defined in the interval ( 1, < < 0 ( )= 1, 0 < < The appropriate Fourier series expansion for ( ) is (A) (B) (C) (D) < < ) as: f ( x ) 4 / [sin x (sin 3 x ) / 3 (sin 5 x ) / 5 ...] f ( x ) 4 / [sin x (sin 3 x ) / 3 (sin 5 x ) / 5 ...] f ( x ) 4 / [cos x (cos 3 x ) / 3 (cos 5 x ) / 5 ...] f ( x ) 4 / [cos x (cos 3 x ) / 3 (cos 5 x ) / 5 ...] Q.37 Atoms, which can be assumed to be hard spheres of radius R, are arranged in an fcc lattice with lattice constant a, such that each atom touches its nearest neighbours. Take the center of one of the atoms as the origin. Another atom of radius r (assumed to be hard sphere) is to be accommodated at a position (0, a/2, 0) without distorting the lattice. The maximum value of r/R is ________. (Give your answer upto two decimal places) Q.38 In an inertial frame of reference S, an observer finds two events occurring at the same time at coordinates x1 0 and x 2 d . A different inertial frame S moves with velocity v with respect to S along the positive x-axis. An observer in S also notices these two events and finds them to occur and t 2 and at positions x1 and x 2 , respectively. If t t 2 t1 , x x 2 x1 and at times t1 1 v2 1 2 c , which of the following statements is true ? (A) t 0, x d (C) t vd c 2 , x d PH (B) t 0, x d (D) t vd c 2 , x d 5/10 The energy vs. wave vector E k relationship near the bottom of a band for a solid can be GATE 2016 Physics Q.39 approximated as E A(ka) B(ka) , where the lattice constant a = 2.1 . The values of A and 2 4 B are 6.3 10 19 J and 3.2 10 20 J, respectively. At the bottom of the conduction band, the ratio of the effective mass of the electron to the mass of free electron is _______. (Give your answer upto two decimal places) (Take =1.05x10-34 J-s, mass of free electron= 9.1x10-31 kg) Q.40 E ( z , t ) E0 cos(k z t )i . The Poynting vector for the wave is The electric field component of a plane electromagnetic wave travelling in vacuum is given by 2 cos 2 (k z t ) j (A) c 0 / 2 E0 2 cos 2 ( k z t )k (B) c 0 2 E 0 2 2 j (C) c 0 E0 cos (k z t ) 2 2 (D) c 0 E0 cos (k z t )k Q.41 Q.42 Consider a system having three energy levels with energies 0, 2 and 3 , with respective degeneracies of 2, 2 and 3. Four bosons of spin zero have to be accommodated in these levels such that the total energy of the system is 10 . The number of ways in which it can be done is ________. The Lagrangian of a system is given by L 1 2 2 2 mgl cos , where m, l and g are constants. ml sin 2 2 Which of the following is conserved? sin (A) 2 Q.43 PH sin (B) (C) sin (D) sin 2 Protons and -particles of equal initial momenta are scattered off a gold foil in a Rutherford scattering experiment. The scattering cross sections for proton on gold and -particle on gold are p and respectively. The ratio p is ________. 6/10 GATE 2016 Physics Q.44 For the digital circuit given below, the output X is A X B C (A) A B C (C) A (B C) Q.45 X 7 AX , 8 Y 5 AY 1 5 A (C) X , X Y 7 AY 8 X 7 AX 1 , Y 5 AY 8 5 A (D) X , X 8 Y 7 AY (B) A two-level system has energies zero and E . The level with zero energy is non-degenerate, while the level with energy E is triply degenerate. The mean energy of a classical particle in this system at a temperature T is Ee E / k BT 1 3e E / k BT 3Ee E / k BT (C) 1 e E / k BT (A) PH (D) A (B C) The Fermi energies of two metals X and Y are 5 eV and 7 eV and their Debye temperatures are 170 K and 340 K, respectively. The molar specific heats of these metals at constant volume at low temperatures can be written as C V X X T AX T 3 and CV Y Y T AY T 3 , where and A are constants. Assuming that the thermal effective mass of the electrons in the two metals are same, which of the following is correct? (A) Q.46 (B) A (B C) Ee E / k BT 1 e E / k BT 3Ee E / k BT (D) 1 3e E / k BT (B) 7/10 GATE 2016 Physics Q.47 A particle of rest mass M is moving along the positive x-direction. It decays into two photons 1 Q.48 If x and p are the x components of the position and the momentum operators of a particle and 2 as shown in the figure. The energy of 1 is 1 GeV and the energy of 2 is 0.82 GeV. The value of M (in units of GeV/c2) is ________. (Give your answer upto two decimal places) 2 2 respectively, the commutator [ x , p ] is (A) i ( xp px ) (C) i ( xp px ) Q.49 . The magnetic field in the Bz k permeability r . The magnetic field in the free space is B x i magnetic material is The x-y plane is the boundary between free space and a magnetic material with relative (A) (C) Q.50 (B) 2i ( xp px ) (D) 2i ( xp px ) Bz k Bx i r Bz k (B) B x i Bz k (D) r B x i 1 Bz k Bx i r Let l, m be the simultaneous eigenstates of L2 and L z . Here L is the angular momentum operator with Cartesian components ( L x , L y , L z ) , l is the angular momentum quantum number and m is the azimuthal quantum number. The value of 1,0 ( Lx iL y ) 1, 1 is (B) (A) 0 Q.51 (C) 2 (D) 3 For the parity operator P, which of the following statements is NOT true? (A) = (B) P 2 P (C) P 2 I (D) = GATE 2016 Physics Q.52 For the transistor shown in the figure, assume VBE = 0.7 V and is _________. (Give your answer upto one decimal place) Q.53 The state of a system is given by = 100. If Vin = 5V, Vout (in Volts) 1 2 2 3 3 where 1 , 2 state 2 Q.54 dc and 3 form an orthonormal set. The probability of finding the system in the is ________. (Give your answer upto two decimal places) According to the nuclear shell model, the respective ground state spin-parity values of 17 8 O nuclei are 1 1 , 2 2 3 5 (C) , 2 2 (A) 1 5 , 2 2 3 1 (D) , 2 2 (B) 15 8 O and GATE 2016 Physics Q.55 A particle of mass m and energy E, moving in the positive x direction, is incident on a step potential at x = 0, as indicated in the figure. The height of the potential is V0, where V0 > E. At x x0 , where x0 0 , the probability of finding the electron is 1/e times the probability of finding it at x = 0. If 2m(V0 E ) , the value of x0 is 2 V0 E x=0 (A) 2 (B) 1 (C) x = x0 1 2 (D) 1 4 END OF THE QUESTION PAPER PH 10/10 Q. No 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Type Section Key Marks MCQ GA B 1 MCQ GA A 1 MCQ GA D 1 MCQ GA C 1 MCQ GA B 1 MCQ GA C 2 MCQ GA C 2 MCQ GA C 2 MCQ GA A 2 MCQ GA C 2 MCQ PH D 1 MCQ PH C 1 MCQ PH C 1 NAT PH 0:0 1 MCQ PH A 1 MCQ PH B 1 NAT PH 4:4 1 NAT PH 0.25 : 0.25 1 NAT PH 0.5 : 0.5 1 MCQ PH A 1 NAT PH 2:2 1 MCQ PH A 1 NAT PH 9:9 1 MCQ PH C 1 MCQ PH A 1 MCQ PH B 1 NAT PH 1.72 : 1.74 1 NAT PH 400 : 400 1 NAT PH 2.41 : 2.49 1 MCQ PH B 1 MCQ PH B 1 MCQ PH A 1 NAT PH 2:2 1 NAT PH 2:2 1 MCQ PH C 1 MCQ PH D 2 NAT PH 12 : 12 ; 6 : 6 2 MCQ PH C 2 MCQ PH B 2 NAT PH 24 : 24 2 NAT PH 80 : 80 2 MCQ PH D 2 MCQ PH B 2 MCQ PH C 2 NAT PH 26.65 : 26.68 2 MCQ PH A 2 NAT PH 0.40 : 0.42 2 MCQ PH C 2 NAT PH 0.20 : 0.24 2 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 MCQ NAT MCQ NAT MCQ MCQ MCQ NAT MCQ MCQ MCQ MCQ NAT NAT MCQ MCQ PH PH PH PH PH PH PH PH PH PH PH PH PH PH PH PH D 18 : 18 A 4:4 B A D 1.40 : 1.45 D D C B 5.5 : 5.9 0.27 : 0.29 B C 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

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