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100+ Free GATE MA Practice Questions

Pass your Graduate Aptitude Test in Engineering — Mathematics (MA) Paper exam on the first try — instant access, no signup required.

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2026 Statistics

Key Facts: GATE MA Exam

65 questions, 100 marks

GATE MA paper structure (10 GA + 55 MA)

gate2026.iitg.ac.in

180 minutes

Total exam time for GATE MA

GATE 2026 Information Brochure (IIT Guwahati)

INR 1000

Application fee (General) within standard window

GATE 2026 Notification

8 institutes

Conducting institutes (IISc + 7 IITs)

NCB-GATE

100

Free practice questions here

OpenExamPrep

GATE MA is a 180-minute computer-based test with 65 questions for 100 marks (10 GA for 15 marks + 55 MA subject for 85 marks). Mix of MCQ, MSQ, and NAT. Negative marking on MCQs only (1/3 for 1-mark, 2/3 for 2-mark). GATE 2026 by IIT Guwahati.

Sample GATE MA Practice Questions

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

1If the average of five consecutive odd numbers is 27, what is the largest of these numbers?
A.29
B.31
C.33
D.35
Explanation: For five consecutive odd numbers in arithmetic progression with common difference 2, the average equals the middle (third) number. So the middle number is 27, and the numbers are 23, 25, 27, 29, 31. The largest is 31.
2Choose the word that best completes the sentence: 'Her arguments were so ______ that no one in the audience could find a flaw in them.'
A.cogent
B.incoherent
C.verbose
D.tangential
Explanation: Cogent means clear, logical, and convincing. An argument with no flaws would be cogent. The other options describe arguments that would in fact contain flaws or weaknesses.
3A train travels 240 km in 4 hours. If its speed is increased by 20 km/h, how long will it take to cover the same distance?
A.2 hours
B.3 hours
C.3 hours 12 minutes
D.3 hours 30 minutes
Explanation: Original speed = 240/4 = 60 km/h. New speed = 60 + 20 = 80 km/h. New time = 240/80 = 3 hours.
4Which number does not belong with the others: 121, 169, 225, 289, 326?
A.121
B.169
C.289
D.326
Explanation: 121 = 11², 169 = 13², 225 = 15², 289 = 17² are all perfect squares of odd numbers. 326 is not a perfect square (√326 ≈ 18.06), so it does not belong.
5In a class of 60 students, 35 study Mathematics, 28 study Physics, and 15 study both. How many study neither?
A.12
B.15
C.18
D.20
Explanation: By inclusion-exclusion, students studying at least one subject = 35 + 28 - 15 = 48. Students studying neither = 60 - 48 = 12.
6If 8 workers can complete a task in 15 days, how many workers are needed to complete the same task in 6 days, assuming equal work rate?
A.16
B.18
C.20
D.24
Explanation: Total work = 8 × 15 = 120 worker-days. To finish in 6 days, required workers = 120/6 = 20.
7Identify the statement that logically follows: All mathematicians are logical. Some philosophers are mathematicians. Therefore,
A.All philosophers are logical.
B.Some philosophers are logical.
C.No philosophers are logical.
D.All logical people are philosophers.
Explanation: From 'All mathematicians are logical' and 'Some philosophers are mathematicians', the philosophers who are mathematicians must be logical. Hence, 'Some philosophers are logical' validly follows.
8A shopkeeper marks an item 40 percent above cost and offers a 25 percent discount. What is the percentage profit?
A.5 percent
B.10 percent
C.12 percent
D.15 percent
Explanation: Let cost = 100. Marked price = 140. After 25 percent discount, selling price = 140 × 0.75 = 105. Profit = 105 - 100 = 5, so 5 percent.
9Complete the series: 2, 6, 12, 20, 30, ?
A.40
B.42
C.44
D.48
Explanation: The nth term is n(n+1): 1·2=2, 2·3=6, 3·4=12, 4·5=20, 5·6=30, 6·7=42. So the next term is 42.
10If 'CRICKET' is coded as 'DSJDLFU', how is 'HOCKEY' coded?
A.IPDLFZ
B.IPDFKZ
C.JPDLFZ
D.IPCLFZ
Explanation: Each letter shifts forward by 1: C→D, R→S, I→J, C→D, K→L, E→F, T→U. Applying +1 to HOCKEY: H→I, O→P, C→D, K→L, E→F, Y→Z, giving IPDLFZ.

About the GATE MA Exam

GATE Mathematics (MA) is one of 30 papers in the Graduate Aptitude Test in Engineering, jointly conducted by the seven IITs and IISc Bangalore on behalf of the National Coordination Board (NCB), Department of Higher Education, MoE, Government of India. The MA paper is a computer-based test of 3 hours with 65 questions worth 100 marks — 10 General Aptitude questions (15 marks) plus 55 subject questions (85 marks) covering Calculus, Linear Algebra, Real and Complex Analysis, ODEs, Algebra, Functional Analysis, Numerical Analysis, PDEs, Topology, and Linear Programming. The format is a mix of Multiple Choice (MCQ), Multiple Select (MSQ), and Numerical Answer Type (NAT). GATE 2026 is being conducted by IIT Guwahati on the first two weekends of February 2026.

Questions

100 scored questions

Time Limit

180 minutes (3 hours)

Passing Score

Qualifying marks: typically 25/100 or μ + σ (whichever is higher), varies yearly by category

Exam Fee

INR 1000 (General/OBC/EWS); INR 500 (SC/ST/PwD/Women) within standard window for GATE 2026 (Joint NCB-GATE — Indian Institutes of Technology and IISc; GATE 2026 conducted by IIT Guwahati)

GATE MA Exam Content Outline

15%

General Aptitude (GA)

Verbal, quantitative, analytical, and spatial aptitude — 10 questions (5×1 mark + 5×2 marks). Common to all GATE papers

~10%

Calculus

Functions of one and several variables, limits, continuity, differentiability, MVT, Taylor series, maxima/minima, multiple integrals, vector calculus (gradient, divergence, curl, Green's/Stokes'/Gauss's theorems)

~10%

Linear Algebra

Vector spaces, linear transformations, rank, nullity, eigenvalues/eigenvectors, Cayley-Hamilton, inner product spaces, orthogonality, quadratic forms

~10%

Real Analysis

Sequences and series, uniform convergence, Riemann integration, bounded variation, Lebesgue measure and integral

~8%

Complex Analysis

Analytic functions, Cauchy-Riemann, complex integration, Cauchy's theorem/integral formula, Taylor and Laurent series, residue theorem, contour integration

~8%

Ordinary Differential Equations

First/higher-order linear ODEs, systems, series solutions (Bessel, Legendre), Sturm-Liouville problem, Laplace transforms

~8%

Algebra

Groups, cyclic groups, cosets, Lagrange's theorem, normal subgroups, quotient groups, homomorphism, rings, ideals, fields, finite fields

~7%

Functional Analysis

Banach spaces, Hilbert spaces, bounded linear operators, Hahn-Banach, open mapping, closed graph theorems

~8%

Numerical Analysis

Root finding (bisection, Newton-Raphson), interpolation, numerical integration (Simpson, trapezoidal), Euler/Runge-Kutta for ODEs, iterative methods (Jacobi, Gauss-Seidel)

~6%

Partial Differential Equations

First-order PDEs (characteristics), classification of second-order PDEs, heat/wave/Laplace equations, separation of variables

~5%

Topology

Basic topology, metric spaces, compactness, connectedness

~5%

Linear Programming

LPP, simplex method, duality, transportation and assignment problems

How to Pass the GATE MA Exam

What You Need to Know

  • Passing score: Qualifying marks: typically 25/100 or μ + σ (whichever is higher), varies yearly by category
  • Exam length: 100 questions
  • Time limit: 180 minutes (3 hours)
  • Exam fee: INR 1000 (General/OBC/EWS); INR 500 (SC/ST/PwD/Women) within standard window for GATE 2026

Keys to Passing

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

GATE MA Study Tips from Top Performers

1Master the standard NPTEL/NCERT M.Sc. textbooks first — Rudin (Real & Complex Analysis), Hoffman-Kunze (Linear Algebra), Herstein (Algebra), Conway (Functional Analysis), Sastry (Numerical Analysis)
2Solve at least 10 years of previous GATE MA papers (2015 onwards) under timed conditions — patterns repeat, especially in Linear Algebra and Calculus
3Practice NAT questions ruthlessly — they carry no negative marking, so build speed on numerical computation (eigenvalues, integration, ODE roots)
4Maintain a formula sheet for ODE solution forms, Laplace transforms, residue formulas, Cayley-Hamilton, and Simpson/RK4 — review daily in the final 30 days
5Take at least 20-25 full-length mocks across the 3-month preparation phase; the official virtual calculator interface on gate2026.iitg.ac.in mirrors the exam exactly
6For Functional Analysis and Topology (newer additions to MA), focus on standard theorem statements and counterexamples — direct theorem-recall questions are common

Frequently Asked Questions

What is the GATE Mathematics (MA) 2026 exam pattern?

GATE MA 2026 is a 3-hour computer-based test with 65 questions totaling 100 marks. The paper has 10 General Aptitude (GA) questions for 15 marks and 55 subject (MA) questions for 85 marks. Question types are MCQ, MSQ (Multiple Select), and NAT (Numerical Answer Type).

What is the marking scheme for GATE MA?

For MCQs: 1-mark questions carry -1/3 negative marking and 2-mark questions carry -2/3 for incorrect answers. MSQs and NAT questions carry NO negative marking, so candidates should always attempt them. Unanswered questions get 0.

Who conducts GATE 2026 and where do I apply?

GATE 2026 is conducted by IIT Guwahati on behalf of the National Coordination Board (NCB)-GATE, jointly by IISc Bangalore and the seven IITs (Bombay, Delhi, Guwahati, Kanpur, Kharagpur, Madras, Roorkee). Apply at the official portal gate2026.iitg.ac.in during the application window (typically Aug-Oct).

What is the application fee for GATE MA 2026?

For GATE 2026 (Indian candidates) the standard fee is INR 1000 for General/OBC/EWS and INR 500 for SC/ST/PwD/Women within the standard window. A late fee of INR 500 applies for extended-window applications. International candidates pay a higher fee.

What is the syllabus for GATE Mathematics 2026?

The GATE MA 2026 syllabus covers Calculus, Linear Algebra, Real Analysis, Complex Analysis, Ordinary Differential Equations, Algebra (group/ring/field theory), Functional Analysis, Numerical Analysis, Partial Differential Equations, Topology, and Linear Programming. The full official syllabus PDF is at gate2026.iitg.ac.in/syllabi.html.

Who is eligible to take GATE MA?

Currently studying in or have completed a Bachelor's degree (3-year or 4-year programmes), Master's degree, or equivalent in any branch of science/arts/commerce/engineering. No upper age limit. Foreign nationals are also eligible. There is no minimum percentage requirement.

What can I do with a GATE MA score?

GATE MA scores are used for admission to M.Sc./M.Tech./PhD programmes in Mathematics at IITs, IISc, NITs and other institutions; for some PSU recruitment; and for international universities (Germany, Singapore) that recognise GATE. The score is valid for 3 years.