GATE 2021 PH – Previous Year Questions with Solutions
All 65 questions of GATE 2021 PH with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Which of the following sentences are grammatically correct? (i) Arun and Aparna are here. (ii) Arun and Aparna is here. (iii) Arun’s families is here.…
- Question 2 – The word PHYLAXIS is shown above the horizontal X-axis in the figure. Which option is its mirror image about the X-axis?
- Question 3 – Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each…
- Question 4 – and are operators such that p q=p-q and p q=pq. Then (9(67))(7(65))=
- Question 5 – Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end. The number of distinct seating…
- Question 6 – A person travels 3 units east and then 4 units south from O to P. From P, the person travels northeast to a point 6 units east of O, then northwest to…
- Question 7 – The author said, “Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it…
- Question 8 – 1. Some football players play cricket. 2. All cricket players play hockey. Which statement logically follows?
- Question 9 – PQRS is a square of side r. The shaded area is the intersection of sectors of circles of radius r centered at S and Q. The probability that a…
- Question 10 – In equilateral triangle PQR, PQ is divided into four equal parts, QR into six and PR into eight. Each part has integer length in cm. The minimum area…
- Question 11 – Choose the graph that best describes the variation of dielectric constant r with temperature T in a ferroelectric material. T C is the Curie…
- Question 12 – A matter wave is represented by (x,y,z,t)=A[i(4x+3y+5z-10 t)], where A is constant. The unit vector along its propagation direction is
- Question 13 – A one-dimensional diatomic lattice consists of alternating atoms P and Q as shown. The separation between adjacent Q atoms is a, and P lies midway…
- Question 14 – Two metal–semiconductor junctions are formed between an n-type semiconductor S and metal M as shown. Their work functions are S and M, with M> S.…
- Question 15 – A small current loop carries a time-dependent sinusoidal current. At a distance r much larger than the loop size, the time-averaged integral of the…
- Question 16 – A solenoid of length L and radius R, with R L, carries a steady current. The magnetic field is uniform inside and zero outside. Choose the variation…
- Question 17 – Assume that 13 N (Z=7) undergoes first-forbidden + decay from its ground state with spin-parity J i i to a final state J f f. The possible values of J…
- Question 18 – An electric-dipole (E1) transition connects an initial nuclear state J i i=2+ to a final state J f f. All possible values of J f f are
- Question 19 – Choose the correct statement.
- Question 20 – Consider a two-dimensional square lattice with lattice constant a. Which of the following wave vectors can lie on Bragg planes where an electronic…
- Question 21 – Light is incident from medium 1 (n 1=1) on medium 2 (n 2=3) as shown. Both have the same magnetic permeability. Let R=I R/I I and T=I T/I I denote…
- Question 22 – For a magnetic material, let H be magnetic field intensity, M magnetization, B magnetic flux density and J b bound current density. Which relations…
- Question 23 – A fermion system has a density of states that increases with energy. With particle number fixed, which statements about its chemical potential and…
- Question 24 – Which atomic spectroscopic terms are allowed? Select all that apply.
- Question 25 – A three-level laser has levels 0, 1 and 2 as shown. Atoms are pumped from 0 to 2; laser emission occurs from 1 to 0. If n i and i denote level…
- Question 26 – Let y n(x) satisfy y n-2xy n+2ny n=0, where n is an integer and primes denote derivatives with respect to x. Which plots of n(x)=e-x2/2y n(x) are…
- Question 27 – The donor concentration in non-degenerate n-type silicon is increased by a factor of 100. Find the shift in the Fermi level at 300 K, in meV, rounded…
- Question 28 – Observers O and O have constant relative speed 0.5c. In units with c=1, O measures events P and Q at (x,y,z,t)=(5,3,5,3) and (5,1,3,5) respectively. O…
- Question 29 – A light source with its intensity peak at wavelength 289.8 nm is calibrated at 10,000 K, the temperature of an equivalent blackbody. Under the same…
- Question 30 – A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface. A point mass m slides without friction along its…
- Question 31 – Three non-interacting bosonic particles, each of mass m, are in a one-dimensional infinite potential well of width a. The energy of the third excited…
- Question 32 – The spacing between consecutive S-branch lines in the rotational Raman spectrum of hydrogen is 243.2\ cm-1. With laser wavelength 514.5 nm, a Stokes…
- Question 33 – The transition shown is between 2D 3/2 and 2P 1/2 in zero external magnetic field. How many spectral lines appear in a weak magnetic field? Give an…
- Question 34 – For the three-level atom shown, the Einstein spontaneous-emission coefficients are A 21=2107\ s-1 and A 10=108\ s-1. If 1014 atoms/cm³ are excited…
- Question 35 – Let a and b be constant vectors, and let r and p be generalized positions and conjugate momenta. For Q= a p and P= b r to form a canonical conjugate…
- Question 36 – The combination of logic gates shown represents which operation?
- Question 37 – In a semiconductor, the effective mass ratio of hole to electron is 2:11 and the average relaxation-time ratio of hole to electron is 1:2. The ratio…
- Question 38 – A spin-1/2 particle is in the state =13pmatrix2+i\\2pmatrix. The probability that measurement gives S x=+/2 is
- Question 39 – An electromagnetic wave E=8(kz- t) y V cm⁻¹ is incident normally from vacuum (n 0=1) onto side 1 of the square slab shown. The slab consists of…
- Question 40 – A point charge +Q of mass m is suspended by a massless inextensible string of length l in free space of permittivity 0. The suspension point is at…
- Question 41 – Two concentric conducting spherical shells have radii a,b and charges +Q,-Q, respectively. Half the space between them is filled with a hemispherical…
- Question 42 – The two sets of nuclear energy levels are shown. Nuclei X and Y have odd and even mass numbers, respectively. Choose the best interpretation.
- Question 43 – Three distinguishable particles each have spin S=1/2, S z=1/2 and corresponding magnetic moments z=. In a magnetic field H along +z, the total energy…
- Question 44 – A particle is in a one-dimensional infinite potential well with walls at x=0 and x=L. A perturbing potential rises linearly from V(0)=0 to V(L)=V 0,…
- Question 45 – A state is (x,t)= 2(x,t)+ 4(x,t), where 2 and 4 are the second and fourth normalized harmonic-oscillator wave functions and is the oscillator angular…
- Question 46 – A one-dimensional harmonic oscillator of angular frequency is in equilibrium at T=(k B)-1. Its non-degenerate levels have energies E n=(n+1/2). The…
- Question 47 – Two atoms can occupy three quantum states with energies 0,,2, in equilibrium at T=(k B)-1. Match CD (classical distinguishable), CI (classical…
- Question 48 – The free energy of a ferromagnet is F=F 0+a 0(T-T C)M2+bM4, where F 0,a 0,b are positive constants, M is magnetization and T C is the Curie…
- Question 49 – A spherical galaxy of total mass M and radius R has a uniform mass distribution. In this idealized situation, which graph best describes the orbital…
- Question 50 – A particle scatters from the Yukawa potential U(r)=-U 0e- r/r, with positive U 0,. In the first Born approximation, how does the scattering amplitude…
- Question 51 – The figure plots inverse magnetic susceptibility 1/ versus temperature T for three materials in their paramagnetic states. T C and T N are the Curie…
- Question 52 – A function f(t) is defined only for t0. Its Laplace and Fourier transforms are L(f;s)= 0 e-stf(t)\,dt, f()= 0 f(t)e-i t\,dt. Which statements are…
- Question 53 – Hermitian matrices P,Q are simultaneously diagonalized by the same invertible matrix R: RPR-1=S 1, RQR-1=S 2, where S 1,S 2 are diagonal. Which…
- Question 54 – A uniform block of mass M slides on a smooth horizontal bar. A mass m hangs from it on an inextensible massless string of length l and oscillates only…
- Question 55 – The Gell-Mann–Okubo baryon mass formula is M=M 0+aY+b[I(I+1)-14Y2], where M 0,a,b are constants, I is isospin and Y is hypercharge. If the mass of…
- Question 56 – The total time derivative of a differentiable function g(q i,t) is added to a Lagrangian: L=L(q i, q i,t)+ddtg(q i,t). Let p i,H and p i,H be the…
- Question 57 – A linear charged-particle accelerator is driven by an alternating voltage at 10 MHz and accelerates electrons. After a few drift tubes the electrons…
- Question 58 – The Coulomb contribution to a nucleus’s binding energy is 18.432 MeV. The uniform spherical charge distribution has radius 3 fm. Find the…
- Question 59 – A two-nucleon system is in a spin-singlet state. The spins are represented by Pauli matrices 1 and 2. Find 1 2 as an integer.
- Question 60 – Define I n= Cdz(z-n)2+2, where n is a positive integer. The contour C runs along the real axis from −100 to 100 and returns on the upper semicircle,…
- Question 61 – The source labels the following normalized hydrogen radial wave function as a “second excited state”: R(r)=124a-3/2 r a e-r/(2a), where a is the Bohr…
- Question 62 – An atomic gas at 300 K has number density n=1020 m⁻³ and ground-state valence configuration f7. Its paramagnetic susceptibility is =m10-11. Find m,…
- Question 63 – The electromagnet shown has a 5 cm air gap and a core of magnetic permeability =20000 0. It is driven by a coil with NI=104 A-turns. Core…
- Question 64 – An atom’s spin S and orbital angular momentum L precess about total J, which precesses about the axis of B 1=2B 0 z. The field is changed to B 2=B 0(…
- Question 65 – Spin–orbit interaction splits the 2P2S transition of lithium, of wavelength 6521 Å, into two lines separated by =0.14 Å. Their positive energy…