GATE 2025 PH – Previous Year Questions with Solutions
All 65 questions of GATE 2025 PH with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Is there any good show television tonight? Select the most appropriate option to complete the above sentence.
- Question 2 – As the police officer was found guilty of embezzlement, he was dismissed from the service in accordance with the Service Rules. Select the most…
- Question 3 – The sum of the following infinite series is: 11!+12!+13!+14!+15!+
- Question 4 – A thin wire is used to construct all the edges of a cube of 1 m side by bending, cutting and soldering the wire. If the wire is 12 m long, what is the…
- Question 5 – The figures I, II and III are parts of a sequence. Which one of the following options comes next in the sequence at IV?
- Question 6 – "Why do they pull down and do away with crooked streets, I wonder, which are my delight, and hurt no man living? Every day the wealthier nations are…
- Question 7 – Rohit goes to a restaurant for lunch at about 1 PM. When he enters the restaurant, he notices that the hour and minute hands on the wall clock are…
- Question 8 – A color model is shown in the figure with color codes: Yellow (Y), Magenta (M), Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K). Which one of…
- Question 9 – A circle with center at (x, y) = (0.5, 0) and radius = 0.5 intersects with another circle with center at (x, y) = (1, 1) and radius = 1 at two points.…
- Question 10 – An object is said to have an n-fold rotational symmetry if the object, rotated by an angle of 2π n, is identical to the original. Which one of the…
- Question 11 – For a two-dimensional hexagonal lattice with lattice constant a, the atomic density is
- Question 12 – Consider a crystal that has a basis of one atom. Its primitive vectors are a 1=a i, a 2=a j, a 3= a2( i+ j+ k), where i, j, k are Cartesian unit…
- Question 13 – A particle of mass m is in a potential V(x)=12m2x2 for x>0 and V(x)= for x0, where is the angular frequency. The ratio of the energies corresponding…
- Question 14 – A particle is scattered from a potential V( r)=g3( r), where g is a positive constant. Using the first Born approximation, the angular (,) dependence…
- Question 15 – The Joule-Thomson expansion of a gas is
- Question 16 – Which one of the following is correct for phase velocity v p and group velocity v g? (c is the speed of light in vacuum)
- Question 17 – As per the Drude model of metals, the electrical resistance of a metallic wire of length L and cross-section area A is (consider as relaxation time, m…
- Question 18 – Which one of the following baryons has strangeness quantum number S= −1?
- Question 19 – A logic gate circuit is shown in the figure below. The correct combination for the input (P, Q) for which the output T= 1 is
- Question 20 – The nuclear energy levels of mirror nuclei are similar. Using this empirical fact alone, the nuclear force can be said to be independent of which one…
- Question 21 – Consider f(z)=1/[z2(z-2)3] of a complex variable z. The residues at z=0 and z=2, respectively, are
- Question 22 – Consider one mole of a monovalent metal at absolute zero temperature, obeying the free electron model. Its Fermi energy is E F. The energy…
- Question 23 – A paramagnetic material containing ions with total angular momentum J=1/2 is kept at absolute temperature T. The ratio of the magnetic field required…
- Question 24 – Which of the following option(s) is/are correct for the ground state of a hydrogen atom?
- Question 25 – Which of the following option(s) is/are correct for photons?
- Question 26 – A schematic Pressure-Temperature diagram of water is shown in the figure. Which of the following option(s) is/are correct?
- Question 27 – Which of the following consideration(s) is/are showing that nuclear beta decay, n → p+ e− + ν̅e, has to be a three-body decay?
- Question 28 – Potential energy of two diatomic molecules P and Q of the same reduced mass is shown in the figure. According to this diagram, which of the following…
- Question 29 – Nuclear radiation emitted from a Co 60 radioactive source is detected by a photomultiplier tube (PMT) coupled to a scintillator crystal. Which of the…
- Question 30 – One mole of an ideal monatomic gas at absolute temperature T undergoes free expansion to double its original volume, so that the entropy change is S…
- Question 31 – A linear dielectric sphere of radius R has a uniform frozen-in polarization along the z-axis. Its center initially coincides with the origin, about…
- Question 32 – The effective magnetic moment (in units of Bohr magneton) for the ground state of an isolated 4f ion with 6 unpaired electrons in the 4f shell…
- Question 33 – Powder X-ray diffraction of a cubic solid with lattice constant a has the (111) diffraction peak at =30. If the lattice expands to 1.25a, the angle…
- Question 34 – Consider a monatomic chain of length 30 cm. The phonon density of states is 1.210-4 s. Assuming the Debye model, the velocity of sound in m/s (rounded…
- Question 35 – The + baryon with spin 3/2, at rest, decays to a proton and a pion (+ p+0). The + has positive intrinsic parity and 0 has negative intrinsic parity.…
- Question 36 – The screened nuclear charge of neutral helium is 1.7e, where e is the electronic charge magnitude. Assuming the Bohr model with E n=-Z2/(2n2) atomic…
- Question 37 – The wire loop shown in the figure carries a steady current I. Each straight section of the loop has length d. A part of the loop lies in xy plane and…
- Question 38 – The figure shows a system of two equal masses m and three massless horizontal springs with spring constants k1 , k2 , k1. Ignore gravity. The masses…
- Question 39 – Two projectile protons P1 and P2 both with spin up (along the +z direction) are scattered from another fixed target proton T with spin up at rest in…
- Question 40 – A thin circular ring of radius R lies in the xy plane centered at the origin, carrying uniform line charge density . The quadrupole contribution to…
- Question 41 – An α particle is scattered from an Au target at rest as shown in the figure. D1 and D2 are the detectors to detect the scattered α particle at an…
- Question 42 – Consider a two-level system with energies +,- and populations N +,N -. The total energy is E and particle number is N=N ++N -. In the thermodynamic…
- Question 43 – Let m, n denote energy eigenstates of a one-dimensional simple harmonic oscillator, with position and momentum operators X, P. The matrix element m P…
- Question 44 – A two-level quantum system has eigenvalues E 1,E 2. A perturbation H= x is introduced, where has energy dimensions, is small and dimensionless, and…
- Question 45 – An electron of mass m and charge q is initially spin up, pmatrix1\\0pmatrix. A constant field B=B 0 j is applied. The Hamiltonian is H=- y, where =qB…
- Question 46 – Three non-identical spin-half particles have Hamiltonian H= A2( S 1+ S 2) S 3, where the spin operators label particles 1,2,3 and A has appropriate…
- Question 47 – Which of the following option(s) is/are correct for a Type I superconductor?
- Question 48 – Consider two hypothetical nuclei X1 and X2 undergoing β decay, resulting in nuclei Y1 and Y2, respectively. The decay scheme and the corresponding JP…
- Question 49 – A charge q is placed a distance d above an infinite grounded conducting plate at z=0. In z>0, = 1+ 2 with 1= q4 0x2+y2+(z-d)2, 2=- q4 0x2+y2+(z+d)2.…
- Question 50 – In coordinates (t,x), a contravariant second rank tensor has Att=P,Axx=Q, all other entries zero. A Lorentz boost in +x with speed v gives A A. Set…
- Question 51 – A particle of mass m and charge q in uniform magnetic field 2B z has L= m2v2+qB(xv y-yv x). With conjugate momenta p x,p y,p z and Hamiltonian H,…
- Question 52 – A bead is constrained to move along a long, massless, frictionless horizontal rod parallel to the x axis. The rod itself is moving vertically upward…
- Question 53 – For a one-dimensional Hamiltonian system, consider the canonical transformation (q,p)(Q=1/p,P=qp2). Which generating function(s) is/are correct?
- Question 54 – The energy of a free relativistic particle of rest mass m moving along x is T. In a potential V(x), H=T+V(x). With speed v, momentum p and Lagrangian…
- Question 55 – Consider I=12 iz4-1(z-a/b)(z-b/a)\,dz, on the unit circle centered at the origin, where a,b>0. Which option(s) is/are correct?
- Question 56 – A neutral conducting sphere of radius R in uniform field E 0 z has outside potential V(r,)=V 0-E 0r(1-R3/r3). Which option(s) is/are correct?
- Question 57 – A point charge q is placed at the origin inside an infinite linear dielectric with relative permittivity r. Which option(s) is/are correct?
- Question 58 – A linear magnetic material in the form of a cylinder of radius R and length L is placed with its axis parallel to the z axis. The cylinder has uniform…
- Question 59 – Cyclotrons accelerate deuterons and alpha particles in the same magnetic field to energies 10 and 20 MeV, respectively. Their masses are M d=2000…
- Question 60 – In the transistor circuit shown, V BE=0.7 V and DC=400. The base current in microampere (rounded off to one decimal place) is
- Question 61 – Consider \1,x,x2\. An orthonormal basis on [-1,1] uses normalization -11x2[f(x)]2dx=1. If the basis is (3/2,5/2x,1221/N(5x2-3)), the value of N (in…
- Question 62 – The Hamiltonian is H(p,q)=p2/(2m)+q2A(q) with real A(q). If m q=-5qA(q) and dA/dq=nA(q)/q, the value of n (in integer) is
- Question 63 – Five identical non-interacting particles of mass m and spin 3/2 are confined to a one-dimensional well of length L. If the lowest total energy is…
- Question 64 – A wheel of mass 4M and radius R has mass 3M uniformly on its thin rim and point mass M at its center. Massless spokes join them. Its center is…
- Question 65 – The figure shows an opamp circuit with a 5.1 V Zener diode in the feedback loop. The opamp runs from ±15 V supplies. If a +1V signal is applied at the…