GATE PH 2016 Question Paper & Solutions

Quantitative & Analytical Aptitude

Consider the linear differential equation .xydx dy  If , 0 at 2 x y then the value of y at x=2 is given by (A) 2e (B) 22 e (C) 2e (D) 22e

Quantitative & Analytical Aptitude

Which of the following magnetic vector potentials gives rise to a uniform magnetic field k Bˆ 0 ? (A) k z Bˆ 0 (B) j x Bˆ0 (C)  j x i yB ˆ ˆ 2 0   (D)  j x i yB ˆ ˆ 2 0 

Quantitative & Analytical Aptitude

The molecule 2 17O is

Quantitative & Analytical Aptitude

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 ________.

Quantitative & Analytical Aptitude

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 (B) 2p-1s (C) 2p-2s (D) 3d-2p

Quantitative & Analytical Aptitude

In the SU(3) quark model, the triplet of mesons     , ,0 has

Quantitative & Analytical Aptitude

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  pm . The value of p is ______.

Quantitative & Analytical Aptitude

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) 3/10

Quantitative & Analytical Aptitude

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 - GA Set-2 3/3

Quantitative & Analytical Aptitude

Which of the following curves represents the function ሾ|ୱ୧୬ (|௫|)|ሿ|) for ߨ ? Here, ݔrepresents the abscissa and ݕrepresents the ordinate. (A) (B) (C) (D) END OF THE QUESTION PAPER 1/10 Q. 1 - Q. 25 carry one mark each.

Nuclear & Particle Physics

Question 11 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 12 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 13 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 14 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 15 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 16 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

The kinetic energy of a particle of rest mass 0m is equal to its rest mass energy. Its momentum in units of c m0 , where c is the speed of light in vacuum, is _______. (Give your answer upto two decimal places)

Solid State Physics

The number density of electrons in the conduction band of a semiconductor at a given temperature is 1910 2 3m . Upon lightly doping this semiconductor with donor impurities, the number density of conduction electrons at the same temperature becomes 2010 4 3m . The ratio of majority to minority charge carrier concentration is ________.

Nuclear & Particle Physics

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 2s , the angular frequency of vibration ω of the two block spring system in 1s is _______. (Give your answer upto two decimal places)

Classical Mechanics

A particle moving under the influence of a central force r k r F  ) ( (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?

Nuclear & Particle Physics

Consider the reaction Mn54 25 + e  Cr54 24 + X . The particle X is (A) γ (B) e (C) n (D) π0

Nuclear & Particle Physics

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

Nuclear & Particle Physics

Consider an elastic scattering of particles in 0l states. If the corresponding phase shift 0 is 090 and the magnitude of the incident wave vector is equal to 2 fm-1 then the total scattering cross section in units of fm2 is _______.

Electromagnetic Theory

A hydrogen atom is in its ground state. In the presence of a uniform electric field ,ˆ0z E E  the leading order change in its energy is proportional to nE ) (0 . The value of the exponent n is _______. 4/10

Nuclear & Particle Physics

A solid material is found to have a temperature independent magnetic susceptibility, .C Which of the following statements is correct?

Electromagnetic Theory

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 (A) k2  (B) k  (C) k k 2 ) 2 ( (D) k k ) 1 (

Nuclear & Particle Physics

The number of spectroscopic terms resulting from the S L coupling of a 3 p electron and a 3 d electron is _______.

Nuclear & Particle Physics

Which of the following statements is NOT correct?

Quantum Mechanics

If 1s and 2s are the spin operators of the two electrons of a He atom, the value of 2 1s s  for the ground state is (A) 2 2 3  (B) 2 4 3  (C) 0 (D) 2 4 1 

Nuclear & Particle Physics

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 2 2 2 2mL  is _______.

Nuclear & Particle Physics

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 ______.

Nuclear & Particle Physics

Let ܸ௜ be the ݅௧௛ component of a vector field ܸሬ⃗, which has zero divergence. If ߲௝ ≡߲/ݔ߲௝, the expression for ߳௜௝௞ ߳௟௠௞ ߲௝߲௟ܸ௠ is equal to (A) i k jV   (B) i k jV  (C) i jV2 (D) i jV2  5/10

Nuclear & Particle Physics

The direction of ∇ሬሬ݂⃗for a scalar field ݂(ݔ,ݕ ,ݖ )= ଵ ଶݔଶ -ݕݔ+ ଵ ଶݖଶ at the point ܲ(1, 1, 2) is (A)   5 ˆ2ˆ k j  (B)   5 ˆ2ˆ k j  (C)   5 ˆ2ˆ k j (D)   5 ˆ2ˆ k j

Quantum Mechanics

zand , y x are the Pauli matrices. The expression x y y x 2 is equal to (A) zi3 (B) zi (C) zi (D) zi3

Nuclear & Particle Physics

A particle of mass ݉= 0.1 kg is initially at rest at origin. It starts moving with a uniform acceleration 2msˆ10  i a at ݐ= 0. The action ܵof the particle, in units of J-s, at ݐ= 2 ݏis ______. (Give your answer upto two decimal places)

Mathematical Physics

A periodic function ݂(ݔ)of period 2ߨis defined in the interval (-ߨ< ݔ< ߨ)as: ݂(ݔ)= ቄ-1, -ߨ< ݔ< 0 1, 0 <ݔ< ߨ T he appropriate Fourier series expansion for ݂(ݔ)is

Nuclear & Particle Physics

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)

Nuclear & Particle Physics

In an inertial frame of reference S, an observer finds two events occurring at the same time at co- ordinates 01 x and .2 d x 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 at times 1t and 2t and at positions 1x and ,2x respectively. If 1 2t t t , 1 2x x x and 2 2v1 1 c   , which of the following statements is true ? (A) d x t , 0 (B) d x t , 0 (C) d x c d t    , v2 (D)  d x c d t   , v2 6/10

Nuclear & Particle Physics

The energy vs. wave vector  k E relationship near the bottom of a band for a solid can be approximated as 42 ) ( ) (ka B ka A E  , where the lattice constant a = 2.1 Å. The values of A and B are J, 10 2 . 3 and J 10 3 . 62019   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)

Electromagnetic Theory

The electric field component of a plane electromagnetic wave travelling in vacuum is given by i t z k E t z Eˆ)cos( ) , (0   . The Poynting vector for the wave is

Quantum Mechanics

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 ________.

Classical Mechanics

The Lagrangian of a system is given by   constants. are and , where , cossin2 1 2 2 2 2 g l mmglml L     Which of the following is conserved? (A)  2sin (B)  sin (C)   sin  (D)   2sin 

Nuclear & Particle Physics

Protons and α-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 α-particle on gold are p and  respectively. The ratio p  is ________. 7/10

Nuclear & Particle Physics

For the digital circuit given below, the output X is (A) C B A  (B) C) (B A  (C) C) (B A  (D) C) (B A 

Nuclear & Particle Physics

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   3T A TC XXXV   and   ,3T A T CYYYV   where γ 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) 8 ,5 7   Y X Y X A A   (B) 8 1,5 7   Y X Y X A A   (C) 8 1,7 5   Y X Y X A A   (D) 8 ,7 5   Y X Y X A A  

Nuclear & Particle Physics

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

Nuclear & Particle Physics

Question 47 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

If x and p are the x components of the position and the momentum operators of a particle respectively, the commutator ] , [2 2p x is (A) ) (px xp i (B) ) ( 2px xp i (C) ) (px xp i (D) ) ( 2px xp i

Electromagnetic Theory

The x-y plane is the boundary between free space and a magnetic material with relative permeability r . The magnetic field in the free space is k B i Bz x ˆˆ . The magnetic field in the magnetic material is (A) k B i Bz x ˆˆ (B) k B i Bz r x ˆˆ  (C) k B i Bz x r ˆˆ1  (D) k B i Bz x r ˆˆ

Quantum Mechanics

Let m l, be the simultaneous eigenstates of 2L and zL . Here L  is the angular momentum operator with Cartesian components ( ) , ,z y xL L L, l is the angular momentum quantum number and m is the azimuthal quantum number. The value of is 1 , 1 ) ( 0 , 1 y xiL L (A) 0 (B)  (C) 2 (D) 3

Electronics

For the parity operator P, which of the following statements is NOT true? (A) ܲற =ܲB) P P 2 (C) I P2 (D) ܲற =ܲିଵ .52 For the transistor shown in the figure, assume VBE = 0.7 V and βdc = 100. If Vin = 5V, Vout (in Volts) is _________. (Give your answer upto one decimal place)

Nuclear & Particle Physics

Question 52 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

The state of a system is given by 321 3 2      where 1 , 2 and 3 form an orthonormal set. The probability of finding the system in the state 2 is ________. (Give your answer upto two decimal places)

Quantum Mechanics

According to the nuclear shell model, the respective ground state spin-parity values of O15 8 and O17 8 nuclei are (A)   2 1,2 1 (B)   2 5,2 1 (C)   2 5,2 3 (D)   2 1,2 3 10/10

Nuclear & Particle Physics

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 V 0 > E. At 0 where ,00  x x x , the probability of finding the electron is 1 /e times the probability of finding it at x = 0. If 2 0 ) ( 2  E V m , the value of x0 is (A)  2 (B)  1 (C) 2 1 (D) 4 1 END OF THE QUESTION PAPER x = x0 V0 E x = 0 Q. No Type Section Key Marks 1 MCQ GA B 1 2 MCQ GA A 1 3 MCQ GA D 1 4 MCQ GA C 1 5 MCQ GA B 1 6 MCQ GA C 2 7 MCQ GA C 2 8 MCQ GA C 2 9 MCQ GA A 2 10 MCQ GA C 2 1 MCQ PH D 1 2 MCQ PH C 1 3 MCQ PH C 1 4 NAT PH 0 : 0 1 5 MCQ PH A 1 6 MCQ PH B 1 7 NAT PH 4 : 4 1 8 NAT PH 0.25 : 0.25 1 9 NAT PH 0.5 : 0.5 1 10 MCQ PH A 1 11 NAT PH 2 : 2 1 12 MCQ PH A 1 13 NAT PH 9 : 9 1 14 MCQ PH C 1 15 MCQ PH A 1 16 MCQ PH B 1 17 NAT PH 1.72 : 1.74 1 18 NAT PH 400 : 400 1 19 NAT PH 2.41 : 2.49 1 20 MCQ PH B 1 21 MCQ PH B 1 22 MCQ PH A 1 23 NAT PH 2 : 2 1 24 NAT PH 2 : 2 1 25 MCQ PH C 1 26 MCQ PH D 2 27 NAT PH 12 : 12 ; 6 : 6 2 28 MCQ PH C 2 29 MCQ PH B 2 30 NAT PH 24 : 24 2 31 NAT PH 80 : 80 2 32 MCQ PH D 2 33 MCQ PH B 2 34 MCQ PH C 2 35 NAT PH 26.65 : 26.68 2 36 MCQ PH A 2 37 NAT PH 0.40 : 0.42 2 38 MCQ PH C 2 39 NAT PH 0.20 : 0.24 2 40 MCQ PH D 2 41 NAT PH 18 : 18 2 42 MCQ PH A 2 43 NAT PH 4 : 4 2 44 MCQ PH B 2 45 MCQ PH A 2 46 MCQ PH D 2 47 NAT PH 1.40 : 1.45 2 48 MCQ PH D 2 49 MCQ PH D 2 50 MCQ PH C 2 51 MCQ PH B 2 52 NAT PH 5.5 : 5.9 2 53 NAT PH 0.27 : 0.29 2 54 MCQ PH B 2 55 MCQ PH C 2

Nuclear & Particle Physics

Question 56 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 57 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 58 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 59 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 60 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 61 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 62 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 63 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 64 from official GATE PH 2016 Examination.

Nuclear & Particle Physics

Question 65 from official GATE PH 2016 Examination.