100+ Free IIT JAM Physics Practice Questions

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A standing wave on a string of length L fixed at both ends has fundamental frequency f₁. The frequency of the third harmonic (third allowed mode) is which value?

f₁

f₁/3

3f₁

2f₁

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2026 Statistics

Key Facts: IIT JAM Physics Exam

60 questions (30 MCQ + 10 MSQ + 20 NAT)

JAM 2026 Physics paper structure for 100 marks

JAM 2026 Information Brochure (IIT Bombay)

INR 1,800

JAM 2026 application fee (General/OBC, one paper)

jam2026.iitb.ac.in

15 February 2026

JAM 2026 exam date

JAM 2026 schedule (IIT Bombay)

21 IITs + IISc

Institutes accepting JAM PH scores for MSc admission

JAM 2026 Admitting Institutes list

100

Free practice questions here

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JAM PH is a 180-minute computer-based test of 60 questions (30 MCQ + 10 MSQ + 20 NAT) for 100 marks. Negative marking applies only to MCQs (-1/3 for 1-mark, -2/3 for 2-mark items). MSc Physics admission at 21 IITs and IISc; JAM 2026 organized by IIT Bombay on 15 February 2026.

Sample IIT JAM Physics Practice Questions

Try these sample questions to test your IIT JAM Physics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the value of the line integral of the vector field F = (y, -x, 0) around the unit circle x² + y² = 1 traversed counter-clockwise in the z = 0 plane?

A.0

B.-2π

C.2π

D.π

Explanation: Using Stokes' theorem, the line integral equals the surface integral of curl F over the enclosed area. Curl F = (0, 0, -2), and the area of the unit disk is π, so the integral equals -2·π = -2π. Equivalently, parameterize x = cos t, y = sin t and compute ∮(y dx − x dy) = -2π directly.

2The Fourier series of the function f(x) = x defined on -π < x < π and extended periodically contains which type of terms?

A.Only cosine terms (it is even)

B.Only sine terms (it is odd)

C.Both sine and cosine terms

D.Only the constant term

Explanation: The function f(x) = x is odd on the interval (-π, π) because f(-x) = -f(x). For odd functions the Fourier coefficients aₙ (including a₀) vanish, leaving only the sine series bₙ = (2/π)∫₀^π x sin(nx) dx = 2(-1)^(n+1)/n.

3If z = x² + iy² and we attempt to find points where f(z) = z is analytic, the Cauchy-Riemann equations require which condition?

A.2x = 2y and 0 = 0, satisfied only on the line x = y

B.All x and y (function is entire)

C.Only at the origin

D.Nowhere in the complex plane

Explanation: Writing f = u + iv with u = x² and v = y², the Cauchy-Riemann equations ∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x give 2x = 2y and 0 = 0. The first holds only along the line x = y, so the function is differentiable only on that line (not analytic anywhere because analyticity requires an open neighborhood).

4What is the Laplace transform of f(t) = t·e^(-2t) for t ≥ 0?

A.1/(s+2)

B.1/(s+2)²

C.1/s²

D.2/(s+2)²

Explanation: Using the shifting theorem, the Laplace transform of t·e^(at) is 1/(s-a)² for Re(s) > a. With a = -2 we get 1/(s+2)². Alternatively, L{t} = 1/s² and the s-shift s → s+2 gives 1/(s+2)².

5The general solution of the second-order ODE d²y/dx² + 4y = 0 is given by which expression?

A.y = A·e^(2x) + B·e^(-2x)

B.y = A·cos(2x) + B·sin(2x)

C.y = A·cos(4x) + B·sin(4x)

D.y = (A + Bx)·e^(-2x)

Explanation: The characteristic equation is r² + 4 = 0, giving complex roots r = ±2i. For complex conjugate roots ±iω the real-form general solution is y = A·cos(ωx) + B·sin(ωx) with ω = 2.

6The Jacobian determinant of the transformation from Cartesian (x, y) to polar (r, θ) coordinates is given by which expression?

A.1

B.r

C.r²

D.1/r

Explanation: With x = r·cos θ and y = r·sin θ, the Jacobian matrix has rows (cos θ, -r·sin θ) and (sin θ, r·cos θ). Its determinant is r·cos²θ + r·sin²θ = r. Therefore dx dy = r dr dθ for area integrals in polar coordinates.

7Compute the divergence of the vector field F = (x², y², z²) at the point (1, 1, 1).

A.3

B.6

C.0

D.9

Explanation: Divergence ∇·F = ∂(x²)/∂x + ∂(y²)/∂y + ∂(z²)/∂z = 2x + 2y + 2z. At (1, 1, 1) this is 2 + 2 + 2 = 6.

8The eigenvalues of the matrix [[3, 1], [1, 3]] are which pair?

A.1 and 3

B.2 and 4

C.-2 and 4

D.0 and 6

Explanation: The characteristic polynomial is det(A − λI) = (3 − λ)² − 1 = λ² − 6λ + 8 = 0. The roots are λ = (6 ± √(36 − 32))/2 = (6 ± 2)/2, giving λ = 2 and λ = 4.

9What is the Taylor expansion of sin(x) about x = 0 up to the fifth-order term?

A.x − x²/2 + x³/6 − x⁴/24 + x⁵/120

B.x − x³/6 + x⁵/120

C.1 − x²/2 + x⁴/24

D.x + x³/6 + x⁵/120

Explanation: The sine function is odd, so its Maclaurin series contains only odd powers. The series is sin x = x − x³/3! + x⁵/5! − ··· = x − x³/6 + x⁵/120 − ···. Each coefficient is ±1/(2n+1)!.

10For a perfect (exact) differential df = M dx + N dy, what condition must M(x, y) and N(x, y) satisfy?

A.∂M/∂x = ∂N/∂y

B.∂M/∂y = ∂N/∂x

C.M = N

D.∂M/∂y + ∂N/∂x = 0

Explanation: If df = M dx + N dy is an exact differential of some f(x, y), then M = ∂f/∂x and N = ∂f/∂y. By the equality of mixed partials (Clairaut's theorem), ∂M/∂y = ∂²f/∂y∂x = ∂²f/∂x∂y = ∂N/∂x. This is the exactness condition.

About the IIT JAM Physics Exam

IIT JAM Physics (PH) is a national-level computer-based entrance examination for admission to two-year MSc, Joint MSc-PhD, MSc-MTech, MSc-PhD Dual Degree, and other postgraduate programmes in physics at 21 IITs and IISc Bangalore. JAM 2026 is being organized by IIT Bombay on 15 February 2026. The Physics paper carries 100 marks across 60 questions in three sections — Section A (30 MCQs), Section B (10 MSQs), and Section C (20 Numerical Answer Type questions) — to be answered in 180 minutes.

Questions

100 scored questions

Time Limit

180 minutes (3 hours)

Passing Score

No fixed pass; merit-based selection with IIT-wise cut-offs

Exam Fee

INR 1800 (General/OBC, one paper); INR 900 (SC/ST/PwD/female) (JAM 2026 organizing institute: IIT Bombay (on behalf of all IITs and IISc))

IIT JAM Physics Exam Content Outline

~12%

Mathematical Methods of Physics

Calculus and multivariable techniques, vector calculus, Fourier series, ODEs, Laplace transforms, complex analysis and residues, matrices and eigenvalues

~15%

Mechanics and General Properties of Matter

Newton's laws, conservation principles, rotational dynamics, gravitation and Kepler's laws, non-inertial frames, elasticity and Poisson's ratio, surface tension and viscosity

~14%

Oscillations, Waves and Optics

SHM and damped/forced oscillations, wave equation, Doppler effect, interference (Young's slit, Newton's rings), diffraction (single slit, grating), polarization

~16%

Electricity and Magnetism

Gauss's law, electrostatics, capacitance and dielectrics, magnetostatics (Biot-Savart, Ampere), Faraday's induction, Maxwell's equations, EM waves, transmission lines

~14%

Kinetic Theory and Thermodynamics

Kinetic theory, Maxwell-Boltzmann distribution, first and second laws, entropy, thermodynamic potentials, phase transitions, quantum statistics (MB/BE/FD)

~16%

Modern Physics

Special relativity (Lorentz transformations, mass-energy), quantum mechanics (Schrödinger equation, hydrogen atom, uncertainty), nuclear physics, atomic spectra

~13%

Solid State Physics, Devices and Electronics

Crystal structure and X-ray diffraction, free electron model, band theory, semiconductors and PN junctions, BJT and FET, digital logic gates and flip-flops

How to Pass the IIT JAM Physics Exam

What You Need to Know

Passing score: No fixed pass; merit-based selection with IIT-wise cut-offs
Exam length: 100 questions
Time limit: 180 minutes (3 hours)
Exam fee: INR 1800 (General/OBC, one paper); INR 900 (SC/ST/PwD/female)

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

IIT JAM Physics Study Tips from Top Performers

1Master the seven JAM PH sections in parallel — neglecting any one section costs many easy marks, since MSQ and NAT questions span the full syllabus

2Practice numerical-answer-type (NAT) problems daily — they have NO negative marking and reward students who can compute answers precisely without options to fall back on

3Solve at least 15-20 full-length JAM PH mock tests in the 3 months before the exam to build the stamina for 180 minutes of focused problem-solving

4Use authoritative textbooks: Griffiths (EM, QM), Kleppner-Kolenkow (Mechanics), Reif (Thermo/Stats), Hecht (Optics), Kittel (Solid State), Krane (Modern Physics)

5Carefully study past 10 years of JAM PH papers — questions on Gauss's law, Bohr model, Schrödinger equation in 1D, and basic op-amp/diode circuits repeat almost every year with small variations

6For MSQ section, remember that ALL correct options must be selected to earn 2 marks — partial credit is zero, so be conservative and only mark options you are confident about

Frequently Asked Questions

What is the IIT JAM 2026 Physics exam pattern?

JAM PH 2026 is a 180-minute computer-based test with 60 questions for 100 marks. Section A has 30 multiple-choice questions (1 or 2 marks each, with negative marking of -1/3 or -2/3 respectively). Section B has 10 multiple-select questions (2 marks each, all correct options required, no negative marking). Section C has 20 numerical-answer-type questions (1 or 2 marks each, no negative marking).

When is JAM 2026 being held, and which institute is organizing it?

JAM 2026 is being conducted by IIT Bombay on 15 February 2026 across multiple cities in India. The Physics (PH) paper is one of seven JAM 2026 test papers. The official website is jam2026.iitb.ac.in and the JAM 2026 application portal opened in early September 2025.

What is the JAM 2026 application fee?

The application fee for JAM 2026 is INR 1,800 for one test paper for General/OBC-NCL/EWS male candidates, and INR 900 for SC/ST/PwD and female candidates. For two test papers the fees are INR 2,500 and INR 1,250 respectively. Payment is via online modes through the JOAPS portal.

What MSc programmes accept JAM Physics scores?

JAM PH scores are used for admission to two-year MSc in Physics and related programmes (Joint MSc-PhD, MSc-MTech, MSc-PhD Dual Degree) at the 21 IITs, IISc Bangalore, and IISER campuses (some accept JAM separately). Major IIT MSc Physics intakes are at IIT Bombay, Delhi, Madras, Kanpur, Kharagpur, Roorkee, Guwahati, BHU (Varanasi), and ISM Dhanbad.

What is the JAM PH syllabus?

The JAM 2026 Physics syllabus has 7 sections: (1) Mathematical Methods of Physics, (2) Mechanics and General Properties of Matter, (3) Oscillations, Waves and Optics, (4) Electricity and Magnetism, (5) Kinetic Theory and Thermodynamics, (6) Modern Physics (special relativity, quantum mechanics, nuclear/atomic), and (7) Solid State Physics, Devices and Electronics.

How are merit lists prepared and what cut-offs are typical?

JAM merit lists are prepared based on the AIR (All India Rank) derived from raw scores. Cut-offs vary by IIT, programme, and category each year. For IIT Bombay/Madras/Delhi MSc Physics, top general-category candidates typically need AIRs in the top 50-100. Each admitting institute publishes its category-wise cut-off after results.

Can a B.Sc. final-year student apply for JAM 2026?

Yes. Final-year undergraduate students can appear for JAM 2026 provided they complete the qualifying degree before the IIT admission cut-off date (typically 30 September 2026 for JAM 2026). The minimum qualifying-degree marks requirement is set by each admitting institute; IITs typically require at least 55-60% aggregate.