100+ Free IIT JAM MA Practice Questions

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Question 1

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Which of the following sets is NOT a group under the given operation?

(ℝ, +)

(ℤ, +)

(ℚ, +)

(ℝ, ·)

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2026 Statistics

Key Facts: IIT JAM MA Exam

60 questions / 100 marks

JAM MA paper size and marking

jam2026.iitb.ac.in

180 minutes

Total exam time (CBT)

JAM 2026 Information Brochure

INR 1800 / INR 900

Application fee (General / Reserved) for JAM 2026

IIT Bombay JAM 2026 portal

15 February 2026

JAM 2026 exam date

jam2026.iitb.ac.in

100

Free practice questions here

OpenExamPrep

JAM Mathematics (MA) is a 3-hour, 60-question, 100-mark CBT with 30 MCQs (negative marking), 10 MSQs, and 20 NATs (no negative marking). Scores are used by IITs and IISc for MSc Mathematics admission. JAM 2026 fee is INR 1800 (general) / INR 900 (reserved).

Sample IIT JAM MA Practice Questions

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

1Let aₙ = (3n² + 5n + 2) / (n² + 7). What is the limit of the sequence (aₙ) as n → ∞?

A.0

B.3

C.5/7

D.Divergent

Explanation: Divide numerator and denominator by n². aₙ = (3 + 5/n + 2/n²) / (1 + 7/n²). As n → ∞, the 1/n and 1/n² terms vanish, giving 3/1 = 3. The limit exists and equals 3, so the sequence converges.

2Which of the following statements about the sequence aₙ = (-1)ⁿ (1 + 1/n) is true?

A.It converges to 1

B.It converges to -1

C.It is divergent but bounded

D.It is unbounded

Explanation: The sequence oscillates: even terms approach 1 (from above) and odd terms approach -1 (from below). Since the subsequential limits differ, the sequence diverges. However |aₙ| ≤ 2 for all n, so it is bounded. Bounded but non-convergent is the standard behavior for alternating-with-amplitude sequences.

3A sequence (aₙ) is a Cauchy sequence in ℝ if and only if which condition holds?

A.(aₙ) is monotone

B.(aₙ) is bounded

C.(aₙ) is convergent

D.lim aₙ = 0

Explanation: In ℝ (which is complete), every Cauchy sequence converges and every convergent sequence is Cauchy. This equivalence is the completeness property of the real numbers — it fails in ℚ, where Cauchy sequences may converge to irrationals.

4The series Σ (from n=1 to ∞) 1/n^p converges if and only if:

A.p > 0

B.p ≥ 1

C.p > 1

D.p < 1

Explanation: This is the p-series test. By the integral test, ∫₁^∞ x^(-p) dx is finite if and only if p > 1. At p = 1 we get the harmonic series, which diverges; for p < 1 the terms decay too slowly.

5Consider the alternating series Σ (-1)ⁿ⁺¹ / n. Which statement is correct?

A.Diverges

B.Converges absolutely

C.Converges conditionally

D.Sum equals 1

Explanation: By the Leibniz (alternating series) test, since 1/n is positive, decreasing, and tends to 0, the series converges; its sum is ln 2. However Σ 1/n is the harmonic series, which diverges, so the original series does not converge absolutely — making it conditionally convergent.

6Using the ratio test, for which values of x does the series Σ (from n=0 to ∞) xⁿ / n! converge?

A.Only x = 0

B.|x| < 1

C.|x| ≤ 1

D.All x ∈ ℝ

Explanation: Apply the ratio test: |aₙ₊₁/aₙ| = |x|^(n+1)/(n+1)! · n!/|x|ⁿ = |x|/(n+1) → 0 as n → ∞. Since the limit is 0 < 1 for every x, the series converges for all real x. In fact this series equals eˣ.

7Let f(x) = x² sin(1/x) for x ≠ 0 and f(0) = 0. Which statement is true?

A.f is not continuous at 0

B.f is continuous but not differentiable at 0

C.f is differentiable at 0 with f'(0) = 0

D.f is differentiable at 0 with f'(0) = 1

8By the Intermediate Value Theorem, which equation must have a solution in (0, 1)?

A.x⁵ + x - 1 = 0

B.x² + 1 = 0

C.1/x = 0

D.sin(x) = 2

Explanation: Let f(x) = x⁵ + x - 1. Then f(0) = -1 < 0 and f(1) = 1 > 0, with f continuous on [0,1]. By the IVT, f takes the value 0 somewhere in (0, 1). The polynomial is continuous everywhere, so IVT applies.

9By the Mean Value Theorem applied to f(x) = ln(x) on [1, e], there exists c such that f'(c) equals what value?

A.1

B.1/(e - 1)

C.1/e

D.(e - 1)/e

Explanation: MVT states f'(c) = [f(e) - f(1)]/(e - 1) = (1 - 0)/(e - 1) = 1/(e - 1). Since f'(x) = 1/x, solving 1/c = 1/(e - 1) gives c = e - 1, which indeed lies in (1, e).

10What is the second-order Taylor polynomial of f(x) = eˣ about x = 0?

A.1 + x

B.1 + x + x²

C.1 + x + x²/2

D.x + x²/2

Explanation: Taylor's theorem: P₂(x) = f(0) + f'(0)x + f''(0)x²/2. For eˣ, all derivatives at 0 equal 1, giving 1 + x + x²/2. The next term would be x³/6.

About the IIT JAM MA Exam

The IIT JAM (Joint Admission Test for Masters) Mathematics paper, coded MA, is a national-level computer-based test conducted by the IITs and IISc to admit candidates to MSc, MSc-PhD dual, MSc-MTech, and other postgraduate science programmes. JAM 2026 was organized by IIT Bombay and held on 15 February 2026. The MA paper contains 60 questions worth 100 marks in three sections: Section A (30 multiple-choice questions, 10 of 1 mark and 20 of 2 marks), Section B (10 multiple-select questions, all 2 marks each), and Section C (20 numerical-answer-type questions, 10 of 1 mark and 10 of 2 marks). Negative marking applies only to Section A: -1/3 mark for each wrong 1-mark MCQ and -2/3 mark for each wrong 2-mark MCQ. Sections B and C carry no negative marking. The official syllabus covers real analysis, multivariable calculus, vector calculus, ordinary differential equations, linear algebra, and basic abstract algebra.

Questions

100 scored questions

Time Limit

180 minutes (3 hours)

Passing Score

No fixed pass; institute-wise cutoffs by AIR and category

Exam Fee

INR 1800 (General/EWS/OBC); INR 900 (Female/SC/ST/PwD) (Indian Institutes of Technology (IIT Bombay for JAM 2026, rotating annually))

IIT JAM MA Exam Content Outline

~35%

Real Analysis

Sequences (convergence, monotone, Cauchy), series (absolute/conditional convergence, alternating, p-series, ratio/root/integral/comparison tests), functions of one real variable (limits, continuity, IVT, differentiability, Rolle's/MVT/Taylor), Riemann integration and improper integrals

~33%

Multivariable Calculus and Differential Equations

Partial and total derivatives, gradient, chain rule, constrained extrema via Lagrange multipliers; double and triple integrals, change of variables; line, surface, and volume integrals; Green's, Stokes', Gauss's theorems; first-order ODEs (separable, exact, linear, integrating factor), higher-order linear ODEs with constant coefficients, Cauchy-Euler equations, method of undetermined coefficients, variation of parameters, systems of linear ODEs

~32%

Linear Algebra and Algebra

Matrix operations, determinants, rank, inverse, characteristic polynomial, eigenvalues and eigenvectors, diagonalization, Cayley-Hamilton; systems of linear equations and consistency; finite-dimensional vector spaces, basis, dimension, subspaces; linear transformations, kernel, image, rank-nullity theorem; abstract algebra basics — groups, subgroups, cyclic groups, order of element, Lagrange's theorem

How to Pass the IIT JAM MA Exam

What You Need to Know

Passing score: No fixed pass; institute-wise cutoffs by AIR and category
Exam length: 100 questions
Time limit: 180 minutes (3 hours)
Exam fee: INR 1800 (General/EWS/OBC); INR 900 (Female/SC/ST/PwD)

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 MA Study Tips from Top Performers

1Master Real Analysis first — sequence/series convergence, MVT, Taylor's theorem and Riemann integration carry roughly a third of the marks and underpin every other topic

2Practice numerical-answer-type (NAT) questions daily — they carry 30 marks with no negative marking, so accuracy and speed here can swing your rank by 50-100 positions

3For Linear Algebra, drill eigenvalue/eigenvector and rank-nullity problems until you can do 2×2 and 3×3 cases by inspection

4Solve at least 10 full-length JAM MA past papers from 2015 onwards under timed (3-hour) conditions — the question style and difficulty have remained remarkably consistent

5In Section A MCQs, attempt only when you can eliminate at least one option — the -1/3 or -2/3 penalty makes blind guessing a net-negative strategy

6Build a mistake log categorised by topic (real analysis, multivariable, linear algebra, algebra) — most candidates lose marks to sign errors and definition mix-ups, not to advanced concepts

Frequently Asked Questions

What is the IIT JAM Mathematics 2026 exam pattern?

JAM MA is a 3-hour computer-based test with 60 questions worth 100 marks. It has three sections: Section A (30 MCQs — 10 of 1 mark, 20 of 2 marks), Section B (10 multiple-select MSQs of 2 marks each), and Section C (20 numerical-answer-type questions — 10 of 1 mark, 10 of 2 marks). Negative marking applies only to Section A MCQs (-1/3 for 1-mark, -2/3 for 2-mark).

Who conducts IIT JAM and when is JAM 2026 held?

JAM is conducted annually by the IITs and IISc, with the organizing institute rotating each year. JAM 2026 was conducted by IIT Bombay and held on 15 February 2026 (Sunday). The official portal is jam2026.iitb.ac.in, where results, scorecards, and admissions information are published.

What is the application fee for JAM 2026 Mathematics?

For one test paper, JAM 2026 charges INR 1800 for General/EWS/OBC-NCL candidates and INR 900 for Female/SC/ST/PwD candidates. For two papers the fees are INR 2500 and INR 1250 respectively. Late fees apply if registering after the regular deadline.

What topics are in the JAM MA 2026 syllabus?

The syllabus covers three groups: (1) Real Analysis — sequences/series, continuity, differentiability, Riemann integration; (2) Multivariable Calculus and Differential Equations — partial derivatives, multiple integrals, vector calculus (Green's, Stokes', Gauss's), first/higher-order ODEs and systems; (3) Linear Algebra and Algebra — matrices, determinants, eigenvalues, vector spaces, linear transformations, basic group theory (subgroups, cyclic groups, Lagrange's theorem).

Which institutes accept the JAM Mathematics score?

JAM MA scores are used for admission to MSc Mathematics, MSc-PhD Mathematics, Joint MSc-PhD, and integrated programmes at all IITs (Bombay, Delhi, Madras, Kanpur, Kharagpur, Roorkee, Guwahati, Hyderabad, Indore, Mandi, BHU, Patna, Bhilai, Goa, Palakkad, Tirupati, Jodhpur, Dharwad, Ropar, ISM Dhanbad) and at IISc Bangalore. Many NITs, IIEST, IISER, and CFTIs also accept JAM scores.

What rank is needed to get into an IIT MSc Mathematics programme?

Cutoffs vary by institute and category. Historically, top IITs (Bombay, Kanpur, Madras, Delhi) close their general-category MSc Mathematics admission around AIR 100-200, while newer IITs and integrated programmes close at AIR 300-700. Final admission also depends on academic eligibility (BSc with Maths) and category quotas.

Is a calculator allowed in JAM Mathematics?

Physical calculators are not permitted, but the CBT interface provides a virtual on-screen scientific calculator that you can use for all numerical computations. You are also given a scribble pad and pen for rough work; both must be returned at the end of the exam.