GATE 2026 PH – Previous Year Questions with Solutions
All 65 questions of GATE 2026 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 often the numbers. False claims are not going to help. Honesty trust", said the manager. Choose the option with the correct order of words to fill…
- Question 2 – In the sequence of tiles shown below, the missing tile indicated by the question mark should be
- Question 3 – A school has 100 students distributed among 1st to 10th standards. Based on this, which one of the following statements is always correct?
- Question 4 – How many 3-digit numbers can be formed using three distinct single digit prime numbers?
- Question 5 – In a group of students, 10 students like Mathematics, 12 students like English, 4 students like both Mathematics and English, and 6 students like…
- Question 6 – Charity : P :: Retaliation : Q Choose the appropriate pair of words P and Q that fit the analogy.
- Question 7 – A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface…
- Question 8 – Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. The figure is representative. All corners are to be colored such…
- Question 9 – Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them: i. Neither H2 nor H3 is the easternmost hill.…
- Question 10 – As shown in the figure, circle C 1 with center O 1 and radius r 1 touches the square VWXY at points P and Q while circle C 2 with center O 2 and…
- Question 11 – In free space, an electromagnetic wave is travelling whose wavevector is k=10( x+3 y)\ m-1. The electric field component of this electromagnetic wave…
- Question 12 – An infinitely large non-conducting thin sheet in the xy plane (z=0) carries a uniform surface charge density =17.7010-12\ C\,m-2. The electric field…
- Question 13 – Consider an operator A which is not Hermitian. Find the possible values of c and d such that the operator (c A-d A) is Hermitian.
- Question 14 – For a scalar field ( r) and a vector field A( r), ( A) is equivalent to the expression
- Question 15 – Which of the following options is correct for transformation of electric field E and magnetic field B under time reversal, i.e., t-t?
- Question 16 – On a horizontal plane, a projectile of mass m is launched from the ground with speed v 0 at an angle 0 with the horizontal. In addition to the…
- Question 17 – Consider the Otto cycle for an ideal gas engine consisting of two quasistatic adiabatic and two quasistatic isochoric processes. The correct…
- Question 18 – The formula for energy E of a photon gas at temperature T in a two-dimensional box at equilibrium with g 2d() denoting the density of states of…
- Question 19 – For the electric field of an electromagnetic wave given below, which of the following statements is correct? E= x E 0( t)+ y\,2E 0( t+/2)
- Question 20 – A gas of non-interacting 4He atoms (of mass m) is in a three-dimensional trap whose energy levels can be approximated by those of a harmonic…
- Question 21 – Given v 1=12pmatrix1\pmatrix, v 2=12pmatrix1\\-ipmatrix, the tensor product v 1 v 2 is
- Question 22 – Sketch of a two-dimensional vector field V⃗ is shown below. Here, length and arrow head of the arrows denote magnitude and direction of the vector…
- Question 23 – Which one of the following is an allowed process?
- Question 24 – Given Q is the electromagnetic charge and S is the strangeness quantum number, identify the particle(s) for which (Q-S)=0 is satisfied.
- Question 25 – Schematic variation of the specific heat Cp of an ideal gas of diatomic molecules with temperature T is shown in the figure below. For rotational…
- Question 26 – If the perturbation V= x3 is added to the Hamiltonian of a one-dimensional harmonic oscillator, the matrix element m V 0 is/are non-zero for which of…
- Question 27 – For which of the following functions does the Laplacian vanish?
- Question 28 – A projectile of mass m is launched from the ground with the initial speed v 0 at an angle 30° from the horizontal. Take the ground to be horizontal.…
- Question 29 – Consider an electron in the energy eigenstate 211( r) of the hydrogen atom. Given that the radial probability distribution of the electron in such a…
- Question 30 – A dielectric sphere carries a uniform polarization P=26\ C\,cm-2. The magnitude of the electric field at the center of the sphere is E109\ N\,C-1. The…
- Question 31 – Consider a metal-superconductor junction connected to a dc voltage V. At T< Tc, where Tc is the superconductor’s transition temperature, the current I…
- Question 32 – For the energy dispersion of an electron in a one-dimensional solid E(k)=E 0-2(ka), the ratio of the effective mass of the electron in the solid to…
- Question 33 – The specific heat C p(T) of one mole of a material as a function of temperature T is given as C p(T)=AT+BT3, where A=0.695\ mJ\,mol-1K-2 and B=0.045\…
- Question 34 – Raman spectrum of a molecule was recorded using a source of wavelength 5000 Å. The first Stokes line is observed at 5100 Å. The first anti-Stokes line…
- Question 35 – A rocket of length 18.0 m is moving at speed 0.9c (where c is the speed of light) parallel to its own length, relative to the earth. The length of the…
- Question 36 – The function f(z) of complex variable z given below, f(z)=z2-5z+4z3+4z-z2-4, has singular points at z=
- Question 37 – Consider the Pauli matrices x=pmatrix0&1\\1&0pmatrix, y=pmatrix0&-i\&0pmatrix, z=pmatrix1&0\\0&-1pmatrix. The value of Tr( z[ x, y]) is
- Question 38 – Which one of the following statements is true?
- Question 39 – The Hamiltonian for a quantum particle of mass m is given below, where <. The Schrödinger equation for this system can be solved exactly using the…
- Question 40 – Consider two particles with angular momenta j 1=2 and j 2=/2. If the expression j=5/2,m=3/2=c 1 j 1=2,m 1=1 j 2=1/2,m 2=1/2+c 2 j 1=2,m 1=2 j 2=1/2,m…
- Question 41 – The energy E and degeneracy d of the second excited state of a three-dimensional, isotropic quantum harmonic oscillator with angular frequency ω are
- Question 42 – Two identical particles with a fixed total energy E=2 are in thermal equilibrium in a one-dimensional harmonic oscillator potential 12m2x2. Let the…
- Question 43 – In the circuit shown, V(t) = 2 sin(2000πt) Volts, where t is in seconds, which of the following options is correct? (take the opamp to be ideal)
- Question 44 – Considering the circuit and the associated signals measured at different pins (numbered as 1, 2, 3, 4, 5) shown in the figure, the correct option is
- Question 45 – A gas of N classical particles that can occupy energy levels, ε1 and ε2 = ε1 + Δ is in equilibrium with a reservoir at temperature T. From the…
- Question 46 – The Lagrangian L 0=12m q2-12m2q2 with the generalized coordinate q is transformed to L=L 0+df(q)dt. Consider the following statements: (i) Expression…
- Question 47 – An infinitely large thin sheet in the xy-plane carries uniform positive charge density and is moving with constant velocity v in the +x direction (see…
- Question 48 – A positive point charge is fixed at the origin. At some distance from it on the x axis, a point dipole is kept pointing in the +y direction. The force…
- Question 49 – Two frames S (solid lines) and S′ (dashed lines) with common origin are shown in the figure below. Frame S is inertial while S′ is rotating about the…
- Question 50 – Which of the following operators is/are self-adjoint?
- Question 51 – Consider two operators A and B which are related as A=(i B). If is a non-zero real number, which of the following statements is/are true?
- Question 52 – Consider operators A, B, and C for three observables of a quantum system satisfying [ A, B]=0, [ B, C]=0, and [ A, C]0, with uncertainties A, B, C,…
- Question 53 – Consider the distribution of outcomes generated by N (N≫1) independent throws of (i) a coin or (ii) a six-sided dice. A coin (dice) is unbiased if…
- Question 54 – The dispersion (E(k)) of the conduction band (CB) and valence band (VB) for a semiconductor are shown schematically in the figure. Considering the…
- Question 55 – A symmetric rigid body has moment of inertia I1, I2, I3 about its principal axes 1, 2, and 3, respectively, with I1 = I3 = I⊥ and I2 ≠I⊥. It is…
- Question 56 – An particle moves towards a fixed nucleus carrying charge Ze, with initial speed v 0 and impact parameter b. Starting from a large distance from the…
- Question 57 – Consider a particle of mass m=9.010-5 kg and charge q=3.010-4 C in a uniform electromagnetic field E=2 x\ V\,m-1, B=3 z\ V\,m-2s. The particle is…
- Question 58 – Two atomic energy levels differ by 2.2 eV. A gas contains 81020 atoms in the upper level and 51020 in the lower. Ignoring spontaneous emission, the…
- Question 59 – The Hamiltonian of two interacting spin-1/2 particles is H=(A/2) S 1 S 2, where S 1 and S 2 are the spin angular momenta of particles 1 and 2,…
- Question 60 – The output signal (current Id) of a reversed biased (with a voltage Vb) photodiode, on which light is incident, is fed to an amplifier (see figure).…
- Question 61 – A capacitor is made of two circular metal plates of radius 1 m separated by a distance of d=1 mm. The space between them is filled by a dielectric…
- Question 62 – A diatomic molecule has rotational lines spaced by 20.0 cm−1 and moment of inertia I 010-47 kg m². The value of I 0 (one decimal place) is . Given…
- Question 63 – Copper has an electron number density of 8.31028\ m-3. Its Fermi energy in eV (rounded off to one decimal place) is (=1.0610-34 J s, mass of electron…
- Question 64 – Two 1 kg blocks are connected to massless springs of stiffness 8 N/m and 4 N/m on a frictionless floor, as shown, with one spring end fixed to a wall.…
- Question 65 – A 15 cm long scale is held horizontally with one of its ends on the edge of a 1 m high table and the other end resting on one’s index finger. As the…