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UPSC Physics — Previous Year Questions

Every question from Physics papers in UPSC Civil Services Mains (2021–2026), organised by year. 96 questions in total, each with directive-word analysis, model answer points, and a full evaluation rubric.

96Questions
6Years covered

2026 Mains

16 questions · 800 marks

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Paper I 8 Qs · 400 marksPaper II 8 Qs · 400 marks
All 16 questions from 2026

Paper I

  1. Q1 (a) A uniform rod of length L and mass m stands vertically upright on a rough floor and then tips over. What is the… 50 marks
  2. Q2 (a) What is meant by achromatic combination of lenses? Derive the condition for achromatization of a pair of lenses… 50 marks
  3. Q3 (a) The energy of a photon is expressed as E = hν, where h is the Planck's constant and ν is the frequency of the… 50 marks
  4. Q4 (a) (i) In Newton's ring experiment, the space between planoconvex lens and glass plate is filled with a liquid of… 50 marks
  5. Q5 (a) Calculate the effective resistance of the following combination of resistances as shown in the figure and determine… 50 marks
  6. Q6 (a) Discuss the origin of hysteresis in ferromagnetic materials on the basis of domain theory. Explain how domain wall… 50 marks
  7. Q7 (a) A gas has only two particles a and b. Show with the help of diagrams how these two particles can be arranged in… 50 marks
  8. Q8 (a) The space between the plates of a parallel-plate capacitor is filled with a dielectric material whose… 50 marks

Paper II

  1. Q1 (a) (i) The de Broglie wavelength of a particle in thermal equilibrium at a temperature of 27°C is λ. At what… 50 marks
  2. Q2 (a) A particle is in the ground state of a 1-D simple harmonic oscillator potential, V(x) = 1/2 mω²x². Calculate the… 50 marks
  3. Q3 (a) (i) Calculate the number of permitted electrons in a sub-shell and a shell in an atom. (ii) Explain how Pauli's… 50 marks
  4. Q4 (a) (i) What are hot bands in vibrational spectroscopy ? Why are they called so ? (8 marks) (ii) The fundamental and… 50 marks
  5. Q5 (a) Are the nucleons inside the nucleus governed by the laws of quantum physics ? Justify your answer. (10 marks) (b)… 50 marks
  6. Q6 (a) By considering the three-dimensional harmonic oscillator potential, explain the energy levels of nucleons inside… 50 marks
  7. Q7 (a) (i) What is diamagnetism ? Why do diamagnetic materials have negative magnetic susceptibility ? (ii) Discuss the… 50 marks
  8. Q8 (a) (i) Discuss the Debye model of lattice specific heat. What are the limitations of the Debye model ? (10 marks) (ii)… 50 marks

2025 Mains

16 questions · 800 marks

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Paper I 8 Qs · 400 marksPaper II 8 Qs · 400 marks
All 16 questions from 2025

Paper I

  1. Q1 (a) Consider a large stationary cylinder of inner radius R. A smaller solid cylinder of radius r rolls without slipping… 50 marks
  2. Q2 (a) A body moves about a point 'O' under no force, the principal moments of inertia at 'O' being 3A, 5A and 6A. The… 50 marks
  3. Q3 (a) Consider a laser system consisting of an active medium placed between a pair of mirrors forming a resonator. Obtain… 50 marks
  4. Q4 (a) Consider a thick lens of thickness t made of a material of relative refractive index n. Let R₁ and R₂ be the radii… 50 marks
  5. Q5 (a) Consider a point charge of 5 nC placed at a distance of 1 m from a perfect conducting plane (z = 0) of infinite… 50 marks
  6. Q6 (a) Consider a long straight wire of length L carrying a current I. Determine the magnetic vector potential A⃗ at a… 50 marks
  7. Q7 (a) A ternary system consists of three components (A, B and C) in equilibrium with two phases. Determine the number of… 50 marks
  8. Q8 (a) (i) In free space, an electric field (E⃗) is given by the following expression : E⃗ = 10 cos (ω t - 100 x)ĵ V/m… 50 marks

Paper II

  1. Q1 (a) Explain how the uncertainty in position is different from the uncertainty or inaccuracy of the measuring… 50 marks
  2. Q2 (a) What is the density of states? For a relativistic particle of rest mass μ, prove that the density of states in the… 50 marks
  3. Q3 (a) Find out the difference in frequencies of Lyman-alpha line in hydrogen and deuterium atoms. 15 marks (b) The… 50 marks
  4. Q4 (a) State how for spin-half particles, the spin (σ) can be expressed by its three components σ_x, σ_y and σ_z. 20 marks… 50 marks
  5. Q5 (a) Show that the energy of the triplet state (S = 1) is not equal to the energy of the singlet state (S = 0). 10 marks… 50 marks
  6. Q6 (a) The total binding energies of ¹⁵₈O, ¹⁶₈O and ¹⁷₈O are 111·96 MeV, 127·62 MeV and 131·76 MeV respectively. Determine… 50 marks
  7. Q7 (a) What is the minimum energy required to break a ₂He⁴ nucleus into free protons and neutrons? [ Given, m_H = 1·007825… 50 marks
  8. Q8 (a) Classify diamagnetic, paramagnetic and ferromagnetic materials in terms of their magnetic susceptibility (χ). Plot… 50 marks

2024 Mains

16 questions · 800 marks

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Paper I 8 Qs · 400 marksPaper II 8 Qs · 400 marks
All 16 questions from 2024

Paper I

  1. Q1 (a) A particle of mass m kg having an initial velocity V₀ is subjected to a retarding force proportional to its… 50 marks
  2. Q2 (a) (i) Briefly discuss the Kepler's laws of planetary motion. 5 marks (ii) Show that the escape velocity V_e on the… 50 marks
  3. Q3 (a) (i) Explain the phenomenon of double refraction. What are positive and negative crystals? Give their examples. (5… 50 marks
  4. Q4 (a) (i) Write down the system matrix for a combination of two thin lenses in paraxial approximation. Hence obtain the… 50 marks
  5. Q5 (a) In spherical coordinates, V = –25 V on a conductor at r = 2 cm and V = 150 V on another conductor at r = 35 cm. The… 50 marks
  6. Q6 (a) Using Maxwell's equations, obtain Poisson's equation and Laplace's equation. The region -(π)/2 < z/(z₀) < (π)/2 has… 50 marks
  7. Q7 (a) How does Planck's law resolve the ultraviolet catastrophe predicted by classical physics? Calculate the average… 50 marks
  8. Q8 (a) (i) Explain the T-s diagram for the reversible Carnot cycle and hence obtain the expression for the efficiency of… 50 marks

Paper II

  1. Q1 Q1. (a) A particle limited to the x-axis has the wave function φ(x) = bx² between x = 0 and x = 2; the wave function… 50 marks
  2. Q2 Q2. (a) Prove that : (i) [L², Lz] = 0 (ii) [Lz, L+] = ℏL+ (iii) [L+, L-] = 2ℏLz (iv) L+ L- = L² - Lz² + ℏLz where ℏ =… 50 marks
  3. Q3 (a) How do Stokes lines appear in Raman spectrum as per classical and quantum theory of Raman effect ? 20 marks (b)… 50 marks
  4. Q4 (a) (i) Using free electron theory of metals, calculate the Fermi energy level of sodium atom at absolute zero. Assume… 50 marks
  5. Q5 (a) Compare nuclear density of hydrogen (₁H¹) with its atomic density. (Assume the atom to have the radius of its first… 50 marks
  6. Q6 (a) Does the nucleus possess magnetic moment ? Justify your answer. Define nuclear magneton (μN) and Bohr magneton… 50 marks
  7. Q7 (a) (i) What is the origin of paramagnetism? Discuss the temperature dependence of paramagnetic susceptibility. (ii)… 50 marks
  8. Q8 (a) What is nuclear resonance absorption of gamma rays? Describe the working and applications of Mossbauer… 50 marks

2023 Mains

16 questions · 800 marks

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Paper I 8 Qs · 400 marksPaper II 8 Qs · 400 marks
All 16 questions from 2023

Paper I

  1. Q1 (a) A force F⃗ is given by F⃗ = x²y x̂ + zy² ŷ + xz² ẑ. Determine whether or not the force is conservative. 10 marks… 50 marks
  2. Q2 (a) (i) Derive the expressions for gravitational potentials at a point (I) outside the spherical shell, (II) inside the… 50 marks
  3. Q3 (a) (i) What are the requisite conditions for observation of interference pattern on a screen ? (5 marks) (ii) Derive… 50 marks
  4. Q4 (a) Write conditions for working of a step-index optical fiber. In a step-index fiber, the core and cladding materials… 50 marks
  5. Q5 (a) Find the energy stored in a system of four charges Q₁ = 1 nC, Q₂ = 2 nC, Q₃ = 3 nC and Q₄ = 4 nC placed at the… 50 marks
  6. Q6 (a) Two inductors having inductances L₁ and L₂ are connected in parallel. The inductors have a mutual inductance M… 50 marks
  7. Q7 (a) A neutral atom consists of a point nucleus +q surrounded by a uniformly charged spherical cloud (-q) of radius r… 50 marks
  8. Q8 (a) A circular ring of radius R lying on the x-y plane and centred at the origin, carries a uniform line charge λ. Find… 50 marks

Paper II

  1. Q1 (a) Calculate the zero point energy for a particle in an infinite potential well for the following cases : (i) a 100 g… 50 marks
  2. Q2 (a) An operator P describing the interaction of two spin 1/2 particles is P = a + bσ⃗₁·σ⃗₂, where a and b are… 50 marks
  3. Q3 (a) What is vector atom model ? How the principal features of vector atom model were explained by Stern-Gerlach… 50 marks
  4. Q4 (a) A particle constrained to move along x-axis in the domain 0 ≤ x ≤ L has a wave function ψ(x) = sin(nπx/L), where n… 50 marks
  5. Q5 (a) How could you establish that νₑ and ν̄ₑ are two different particles ? 10 marks (b) What is the age of a fossil that… 50 marks
  6. Q6 (a) Establish the Rutherford's scattering cross section formula for α-particle by considering the standard assumptions… 50 marks
  7. Q7 (a) Explain classical theory of diamagnetism. Show that the susceptibility of diamagnetic substances is directly… 50 marks
  8. Q8 (a) What do you understand by the critical size of a reactor ? Explain the main features of nuclear reactors. 5+15=20… 50 marks

2022 Mains

16 questions · 800 marks

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Paper I 8 Qs · 400 marksPaper II 8 Qs · 400 marks
All 16 questions from 2022

Paper I

  1. Q1 (a) An electron is moving under the influence of a point nucleus of atomic number Z. Show that the orbit of the… 50 marks
  2. Q2 (a) Consider two frames of reference S and S′ having a common origin O. The frame S′ is rotating with respect to the… 50 marks
  3. Q3 (a) A homogeneous right triangular pyramid with the base side a and height 3a/2 is shown below. Obtain the moment of… 50 marks
  4. Q4 (a) Consider the diagram below with a water flow rate Q. Derive the expression for Q in terms of the difference in the… 50 marks
  5. Q5 (a) Assume that the Earth's atmosphere is pure nitrogen in thermodynamic equilibrium at a temperature of 300 K… 50 marks
  6. Q6 (a) Write down Maxwell's equations in a non-conducting medium with constant permeability and susceptibility (ρ = j =… 50 marks
  7. Q7 (a) A metal guitar string with a length of 70 cm vibrates at its fundamental frequency of 246.94 Hz in a uniform… 50 marks
  8. Q8 (a) In a partially conducting medium, εᵣ = 18.5, μᵣ = 800 and σ = 1 S m⁻¹. Find α, β, η and the velocity u, for a… 50 marks

Paper II

  1. Q1 (a) What is de Broglie concept of matter wave ? Evaluate de Broglie wavelength of Helium that is accelerated through… 50 marks
  2. Q2 (a) Set up the Schrodinger’s wave equation for one dimensional potential barrier and obtain the probability of… 50 marks
  3. Q3 (a) What is the spin wave function (for s = ½) if the spin component in the direction of unit vector η has a value of… 50 marks
  4. Q4 (a) (i) In a diatomic molecule when one constituent atom is replaced by one of its heavier isotopes, what change takes… 50 marks
  5. Q5 (a) If the nuclear force is charge independent and a neutron and proton form a bound state then why is there no bound… 50 marks
  6. Q6 (a) Show that for a specific value (n, l), there exists a large degeneracy relative to the energy characterized by the… 50 marks
  7. Q7 (a) Explain the drawbacks of Einstein's theory of specific heat and how it was overcome by Debye. (20 marks) (b) A… 50 marks
  8. Q8 (a) Show that for an n-type semiconductor, the Fermi level lies midway between the donor states and the conduction band… 50 marks

2021 Mains

16 questions · 800 marks

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Paper I 8 Qs · 400 marksPaper II 8 Qs · 400 marks
All 16 questions from 2021

Paper I

  1. Q1 (a) A particle moving in a central force field describes the path r = ke^αθ, where k and α are constants. If the mass… 50 marks
  2. Q2 (a) A body of mass m at rest splits into two masses m₁ and m₂ by an explosion. After the split the bodies move with a… 50 marks
  3. Q3 (a) In a step-index optical fiber system, explain the terms pulse dispersion and material dispersion. An optical fiber… 50 marks
  4. Q4 (a) (i) Define moment of inertia and radius of gyration of a body of mass M rotating about an axis. State and prove… 50 marks
  5. Q5 (a) Given that the electric potential of a system of charges is V = 12/r² + 1/r³ volt. Calculate the electric field… 50 marks
  6. Q6 (a) In an inertial reference frame S there is only a uniform electric field E⃗ = 8 kVm⁻¹. Find the magnitude of E⃗' and… 50 marks
  7. Q7 (a) A region 1, z < 0, has a dielectric material with εᵣ = 3·2 and a region 2, z > 0 has a dielectric material with εᵣ… 50 marks
  8. Q8 (a) (i) The melting point of tin is 232°C, its latent heat of fusion is 14 cal/g and the specific heat of solid and… 50 marks

Paper II

  1. Q1 (a) Find the minimum magnetic field needed for the Zeeman effect to be observed in a spectral line of 400 nm wavelength… 50 marks
  2. Q2 (a) Using Pauli spin matrices prove that, (i) σₓσᵧ + σᵧσₓ = 0; σᵧσᵤ + σᵤσᵧ = 0; σₓσᵤ + σᵤσₓ = 0 (ii) σ₊σ₋ = 2(1+σᵤ)… 50 marks
  3. Q3 (a) In observing the Raman spectrum of a sample using 3637Å as the exciting line, one gets stoke line at 3980Å. Deduce… 50 marks
  4. Q4 (a) A particle of rest mass m₀ has a kinetic energy K, show that its de Broglie wavelength is given by λ =… 50 marks
  5. Q5 (a) An X-ray beam of wavelength (λ₁) undergoes a first order Bragg reflection at a Bragg angle of 30°. X-ray of… 50 marks
  6. Q6 (a) What is the importance of study of deuteron ? Obtain the solution of Schrödinger equation for ground state of… 50 marks
  7. Q7 (a) An n-p-n transistor with β = 49 is used in common-emitter amplifier mode with Vcc = 10V and RL = 2 kΩ. If a 100 kΩ… 50 marks
  8. Q8 (a) Sketch the dc load line for the circuit shown. (10 marks) (b) A solid contains a dilute concentration of Nd³⁺ ions… 50 marks

How Physics answers are marked

The shape the examiner expects, what earns the marks and the traps that lose them: the same card our rubrics for this subject are written from.

Answer skeleton

  1. Principle
  2. Setup and diagram
  3. Derivation
  4. Result and limiting case

What earns the marks

  • Draw the labelled diagram first
  • Carry units and check dimensions
  • Derive from first principles where asked
  • Discuss the limiting or special case

What earns the extra mark

  • One line of physical interpretation

Traps that cost marks

  • Formula substitution with no derivation
  • Dropping units
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