GATE 2020 PH – Previous Year Questions with Solutions
All 65 questions of GATE 2020 PH with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – He is known for his unscrupulous ways. He always sheds tears to deceive people.
- Question 2 – Jofra Archer, the England fast bowler, is than accurate.
- Question 3 – Select the word that fits the analogy: Build : Building :: Grow : .
- Question 4 – “I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.” What does “having said that” mean in…
- Question 5 – Define [x] as the greatest integer less than or equal to x, for each x(-,). If y=[x], find the area under y for x[1,4].
- Question 6 – Crowd funding deals with mobilisation of funds for a project from a large number of people, who would be willing to invest smaller amounts through…
- Question 7 – P, Q, R and S are to be uniquely coded using and . If P is coded and Q is coded , then R and S, respectively, can be coded as .
- Question 8 – Find the sum of the first n terms in the sequence 8, 88, 888, 8888, ….
- Question 9 – Select the graph that schematically represents BOTH y=xm and y=x1/m properly in 0 x1, for integral m > 1. The choices are arranged A, B in the top row…
- Question 10 – The bar graph shows students who appeared and passed in an examination for schools P, Q, R and S. Find the average success rate (percentage) of the…
- Question 11 – Which function solves d2u/dx2=k2u for real k?
- Question 12 – A real invertible 33 matrix M has eigenvalues i and eigenvectors e i, i=1,2,3. Which statement is correct?
- Question 13 – A quantum particle has V(x)=0 for -a/2<x<a/2 and V(x)= outside, including the walls. Its ground-state wave function inside the well is proportional to
- Question 14 – For harmonic-oscillator lowering and raising operators a, a, the energy eigenstate n is also an eigenstate of ( a)2 a2. Its eigenvalue is
- Question 15 – Which is a universal logic gate?
- Question 16 – The binary equivalent of hexadecimal F6C is
- Question 17 – The total angular momentum j of the ground state of 17 8 O is
- Question 18 – The strong process is ++p K++X. Given quark content K+=u s, the quark content of X is
- Question 19 – A medium has r>1, r=1 and conductivity >0. It is semi-transparent to an electromagnetic wave when
- Question 20 – A central force is F=-k r/r3, where r points away from the centre. Taking zero potential at infinity, the potential energy is
- Question 21 – Choose the correct relation between Fermi energy E F and chemical potential of a metal.
- Question 22 – A diatomic molecule consists of identical atoms. Let E v and E e be characteristic vibrational nuclear and electronic energies, with electron mass m…
- Question 23 – At an interface of dielectrics with permittivities 1, 2, field lines make angles 1, 2 to the normal as shown. With no free surface charge, which…
- Question 24 – Under parity and time reversal, respectively, the scalar E B is
- Question 25 – A small disk rotates about its suspending fibre. Its small-angle Hamiltonian is H=p 2/(2I)+2/2, with inertia I and restoring torque per unit angle .…
- Question 26 – An insulated container has ideal gas in chamber A and vacuum in chamber B. A plug separating the chambers is removed and the gas fills both. Which…
- Question 27 – Particle A with angular momentum j=3/2 decays into particles B and C of angular momenta j 1,j 2. If 3/2,3/2 A= 1,1 B 1/2,1/2 C, find .
- Question 28 – Far from Earth its magnetic field is approximated by a bar magnet of magnetic pole strength 41014 A m. Suppose a current loop around the magnetic…
- Question 29 – For the two-dimensional lattice shown, find the number of distinct primitive-cell constructions intended by the figure.
- Question 30 – A hydrogenic atom is in a strong magnetic field. Neglect spin–orbit coupling. How many doubly degenerate states arise from its f level?
- Question 31 – A particle Y undergoes strong decay Y-+-. Find its isospin.
- Question 32 – For a counterclockwise contour C: z =1, evaluate 12 i C(z-2z+3z2)dz.
- Question 33 – Let p be conjugate momentum to q. The transformation Q=2\,qm p, P=2\,qm p is canonical. Find m.
- Question 34 – A conducting sphere of radius 1 m is in air. To avoid breakdown, the maximum number of electrons on it is about 710n, with integer n. Find n. Given…
- Question 35 – A particle is constrained to move along a sinusoidal curve. Find its number of degrees of freedom.
- Question 36 – Find the product of the eigenvalues of pmatrix0&0&1\\0&1&0\\1&0&0pmatrix.
- Question 37 – Let e 1=pmatrix1\\0\\0pmatrix, e 2=pmatrix1\\1\\0pmatrix, e 3=pmatrix1\\1\\1pmatrix. For S=\ e 1, e 2, e 3\ in R3, which is correct?
- Question 38 – The spin operator is S x=2pmatrix0&1\\1&0pmatrix. Which statement is correct?
- Question 39 – The input to the shown circuit is V in=2(100t) V and its output is V out=2(100t-/2) V. Given R = 1 kΩ, find C in μF.
- Question 40 – A four-bit ripple counter uses four flip-flops with J = K = 1; each Q output clocks the next flip-flop. Falling clock edges trigger changes. All…
- Question 41 – The Lagrangian is L=a x2+b y2+cxy, with constants a,b,c. For conjugate momenta p x,p y, the Hamiltonian is
- Question 42 – Which matrix does NOT represent a proper rotation in a plane?
- Question 43 – A uniform field B=B 0 y exists in frame K. A perfectly conducting sphere moves at v=v 0 x; its rest frame is K. The field transformations are E =E , E…
- Question 44 – A charge q moving at uniform speed enters a cylindrical region in free space at t = 0 and leaves at t=, as shown. Which graph represents total…
- Question 45 – A one-dimensional non-magnetic crystal has one atom per unit cell. Valence electrons do not interact with one another and interact weakly with ions.…
- Question 46 – In the nuclear Fermi-gas model, nucleons occupy a sphere of radius R=R 0A1/3, where A is mass number. The Fermi energy scales with R 0 as
- Question 47 – A two-dimensional crystal has three atoms in its basis. Find the numbers n of optical and m of acoustic branches of lattice vibrations.
- Question 48 – A system has internal energy U(S,V)= V-2/3S2, where λ is constant, V volume and S entropy. Which equation of state follows?
- Question 49 – A mass m has potential U(x)=a(k2x-/2), with a>0,k2>0. The small-oscillation angular frequency about x = 0 is
- Question 50 – The radial wave function in a central potential is R(r)=A(r/a)e-r/(2a), with normalization constant A and positive constant a. If the most probable…
- Question 51 – A free particle of mass M is in a three-dimensional cubic infinite potential well. Find the degeneracy of its fifth excited energy level.
- Question 52 – The circuit contains a 1 kΩ resistor and three series forward diodes connected from +10.1 V to ground as shown. Each diode drops 0.7 V. Find current I…
- Question 53 – Let u be a relativistic four-velocity satisfying u u =1. With Levi-Civita tensor , evaluate u u u u.
- Question 54 – A simple cubic Bravais lattice with parameter a has a monatomic basis at r 1=0 and r 2=(a/4)( x+ y+ z). The scattering-vector change is K=n 1 G 1+n 2…
- Question 55 – A plane electromagnetic wave of wavelength λ is incident on a circular conducting loop of radius a. Find the angle in degrees between the Poynting…
- Question 56 – A hydrogen electron is in the state n=3,l=2,m=-2. If the variance of its orbital angular-momentum component is ( L y)2=2, find α.
- Question 57 – A vacuum parallel-plate capacitor has sinusoidal applied voltage V(t)=V 0 t. Ignore edge effects. The induced emf within the capacitor can be expanded…
- Question 58 – On - x, write x= k=1 a k kx. Find a 2.
- Question 59 – Let f n(x)=n for -1/(2n) x1/(2n), and zero otherwise. Evaluate n -f n(x) x\,dx.
- Question 60 – Consider H= H 0+ H, with H 0=pmatrixE&0&0\\0&E&0\\0&0&Epmatrix, H=pmatrix0&k&0\&0&k\\0&k&0pmatrix, k>0. If the maximum eigenvalue is 3 eV when E = 2…
- Question 61 – A hydrogen atom is in an orbital angular-momentum state l,m=l. In the vector model, its angular momentum lies on a cone of half-angle 30° to the…
- Question 62 – In the centre-of-mass frame, two protons, each of energy 7000 GeV, collide and produce protons and antiprotons. If proton rest mass is 1 GeV/c², find…
- Question 63 – Hydrogen in the Sun’s atmosphere is at 5800 K. A sample contains 6.0231023 atoms in the ground state. The first excited-state population is…
- Question 64 – A non-interacting gas has speed density f(v)dv=4 v2(m2 k BT)3/2e-mv2/(2k BT)dv. In its corresponding particle-energy distribution, find the most…
- Question 65 – Planck’s spectral energy density is u()=32c3[e/(k BT)-1]. At long wavelengths the spectral energy density varies as T. Find α.