Engineering Mathematics GATE CSE PYQ Topic Wise (2016–2026)

Explore: GATE CS hub · All GATE CS topics · Syllabus & pattern · GATE CS 2026

Answer first

Engineering Mathematics has appeared in 11 of the 11 official GATE CS papers from 2016–2026, with 55 questions in all. It averages 7.2 marks a year, which puts it 7th of 11 technical subjects. The last three papers gave it 8 (2026), 9 (2025), 8 (2024).

The concepts that came back most often are Linear Algebra, Calculus, Probability. Linear Algebra, Calculus, Probability appeared in at least 7 of the 11 years. 51% of the questions are NAT, so you have to work out an exact value with no options to eliminate.

Marks per year

One official set per year (set 1 where GATE CS ran two sessions). Marks are as printed in the official answer key.

Most-asked concepts

Sorted by how many years a concept appeared in, then by marks.

How to practise Engineering Mathematics from these PYQs

1. Start with the concepts at the top of the table above. They repeat, so they pay off first.
2. Open the official PDF for a year, solve only that year’s Engg Maths questions against the clock (about 3 minutes a mark), then check the official key listed below.
3. Log each miss by concept and type (MCQ, MSQ, NAT). An MSQ with one extra option scores zero, so log those separately.
4. Once a concept is clean across two or three years, move on to the next one.
5. Then sit a full year paper from the GATE CS hub so the subject drill turns into exam timing.

Questions by year

Each line gives the official question number, marks, type and concept, our one-line summary and the official key. The full question is in the official PDF linked under each year.

GATE CS 2026 (CS1)

• Q.11 · 1 mark · MCQ · Probability: Pólya urn: chance of equal red and blue balls after two draws (key: B)
• Q.13 · 1 mark · MCQ · Linear Algebra: Maximum multiplicity of an eigenvalue of an n×n real matrix (key: A)
• Q.20 · 1 mark · MSQ · Linear Algebra: Consequences of a standard basis vector in a matrix's null space (key: B, D)
• Q.32 · 1 mark · NAT · Calculus: Constants making a piecewise function continuous at zero (key: 3)
• Q.46 · 2 marks · MSQ · Calculus: Local extrema and differentiability of an absolute-value function (key: A, C, D)
• Q.58 · 2 marks · NAT · Probability: Expected value of a discrete random variable (key: 4.24–4.26)

Paper: official PDF · GATE CS 2026 page

GATE CS 2025 (CS1)

• Q.23 · 1 mark · MSQ · Linear Algebra: Values of k for which a 2x2 linear system has no or infinite solutions (key: A, D)
• Q.31 · 1 mark · NAT · Calculus: Constant that makes a piecewise function differentiable everywhere (key: -2.1–-1.9)
• Q.32 · 1 mark · NAT · Probability: Probability a coin is fake given two heads (Bayes' theorem) (key: 0.49–0.51)
• Q.41 · 2 marks · MCQ · Linear Algebra: Eigenvalues of the 13th power of a 2x2 matrix (key: D)
• Q.56 · 2 marks · NAT · Probability: Probability a 5-bit message arrives correctly over a noisy channel (key: 0.949–0.952)
• Q.58 · 2 marks · NAT · Probability: Probability over an interval for a quadratic density function (key: 0.300–0.302)

Paper: official PDF · GATE CS 2025 page

GATE CS 2024 (CS1)

• Q.11 · 1 mark · MCQ · Calculus: Points where max(x, x cubed) is not differentiable (key: D)
• Q.12 · 1 mark · MCQ · Linear Algebra: Product of eigenvalues of a 3x3 matrix (key: B)
• Q.14 · 1 mark · MCQ · Probability: Independence of order events in a random permutation (key: B)
• Q.27 · 1 mark · MSQ · Probability: Union, independence and conditional probability of two events (key: B, C)
• Q.49 · 2 marks · MSQ · Linear Algebra: Solution space of a homogeneous system with more unknowns than equations (key: A)
• Q.63 · 2 marks · NAT · Probability: Conditional probability of drawing two red balls without replacement (key: 0.370–0.380)

Paper: official PDF · GATE CS 2024 page

GATE CS 2023

• Q.18 · 1 mark · MCQ · Linear Algebra: Relation between determinants of two matrices with permuted rows (key: B)
• Q.28 · 1 mark · MSQ · Calculus: Local maxima and minima of a cubic polynomial (key: B, D)
• Q.30 · 1 mark · NAT · Linear Algebra: Sum of eigenvalues of a graph's adjacency matrix (key: 2 or 4)
• Q.31 · 1 mark · NAT · Calculus: Value of a triple definite integral (key: 0)
• Q.53 · 2 marks · MSQ · Probability: Independence of events defined on two fair coin tosses (key: C, D)

Paper: official PDF · GATE CS 2023 page

GATE CS 2022

• Q.20 · 1 mark · MCQ · Linear Algebra: Whether tr(AB)=tr(BA) holds for rectangular and square matrices (key: C)
• Q.34 · 1 mark · NAT · Calculus: Evaluate a limit as x tends to zero involving an exponential (key: -0.5)
• Q.45 · 2 marks · MCQ · Linear Algebra: Entries of L and U in an LU decomposition of a 3x3 system (key: D)
• Q.53 · 2 marks · MSQ · Linear Algebra: Which vectors are eigenvectors of a given 4x4 matrix (key: A,C,D)

Paper: official PDF · GATE CS 2022 page

GATE CS 2021 (set 1)

• Q.18 · 1 mark · NAT · Probability: Probability an exponential lifetime exceeds its mean (key: 0.35–0.39)
• Q.20 · 1 mark · NAT · Calculus: Value of an infinitely nested square-root expression (key: 0.25)
• Q.35 · 2 marks · MCQ · Probability: Statements about covariance and variance bounds (key: D)
• Q.52 · 2 marks · NAT · Linear Algebra: Largest eigenvalue of a 4x4 0/1 matrix (key: 3)
• Q.54 · 2 marks · NAT · Probability: Conditional probability over a noisy H/L channel (key: 0.04)

Paper: official PDF · GATE CS 2021 page

GATE CS 2020

• Q.1 · 1 mark · MCQ · Calculus: Which functions are increasing everywhere on [0,1] (key: A)
• Q.27 · 2 marks · MCQ · Linear Algebra: Which rank and determinant identities hold for matrices (key: C)
• Q.45 · 2 marks · NAT · Probability: Probability a random 0/1 weighted sum is odd (key: 0.5)

Paper: official PDF · GATE CS 2020 page

GATE CS 2019

• Q.9 · 1 mark · MCQ · Linear Algebra: Relation between invertibility and non-zero determinant (key: D)
• Q.13 · 1 mark · MCQ · Calculus: Evaluate a limit of a rational function at x = 3 (key: C)
• Q.22 · 1 mark · NAT · Probability: Probability two random numbers share the same most significant bit (key: 0.502–0.504)
• Q.44 · 2 marks · NAT · Linear Algebra: Product of eigenvalues of a 4x4 matrix (key: 12)
• Q.46 · 2 marks · NAT · Probability: Expected distance between two random leaves of a full binary tree (key: 4.25)
• Q.47 · 2 marks · NAT · Probability: Probability a quadratic with a uniform coefficient has real roots (key: 0.8)

Paper: official PDF · GATE CS 2019 page

GATE CS 2018

• Q.15 · 1 mark · NAT · Probability: Probability a player wins a dice game with retries on ties (key: 0.021–0.024)
• Q.16 · 1 mark · NAT · Calculus: Evaluate a definite integral numerically (key: 0.27–0.30)
• Q.17 · 1 mark · NAT · Linear Algebra: Largest eigenvalue of a rank-one matrix uv^T (key: 3)
• Q.26 · 2 marks · MCQ · Linear Algebra: Properties of a matrix with a single eigenvector direction (key: D)
• Q.44 · 2 marks · NAT · Probability: Conditional probability from joint temperature distributions (key: 0.60–0.62)

Paper: official PDF · GATE CS 2018 page

GATE CS 2017 (set 1)

• Q.3 · 1 mark · MCQ · Linear Algebra: Nature of solutions of Ax=b given dependent column vectors (key: C)
• Q.19 · 1 mark · NAT · Probability: Expected value of max(X,0) for a zero-mean Gaussian (key: 0.0)
• Q.28 · 2 marks · MCQ · Calculus: Evaluate a limit of a polynomial ratio (key: C)
• Q.30 · 2 marks · MCQ · Linear Algebra: Scalar making a vector sum bisect the angle between vectors (key: A)
• Q.31 · 2 marks · MCQ · Linear Algebra: Eigenvalue bounds for a rank-2 symmetric matrix (key: B)

Paper: official PDF · GATE CS 2017 page

GATE CS 2016 (set 1)

• Q.3 · 1 mark · NAT · Calculus: Evaluate a trigonometric limit (key: 1.0 : 1.0)
• Q.4 · 1 mark · NAT · Probability: Find the lower limit making 1/x^2 a valid density (key: 0.5 : 0.5)
• Q.5 · 1 mark · NAT · Linear Algebra: Determinant of a 3x3 real matrix from known eigenvalues (key: 15.0 : 15.0)
• Q.29 · 2 marks · NAT · Probability: Probability of output from a repeated coin-flip experiment (key: 0.33 : 0.34)

Paper: official PDF · GATE CS 2016 page

Other GATE CS subjects

• General Aptitude
• Discrete Mathematics
• Digital Logic
• Computer Organization & Architecture
• Programming & Data Structures
• Algorithms
• Theory of Computation
• Compiler Design
• Operating Systems
• Databases (DBMS)
• Computer Networks

FAQ

How many marks does Engineering Mathematics carry in GATE CS?

Across the official GATE CS papers from 2016–2026 (one set per year), Engineering Mathematics carried 7.2 marks a year on average, from 5 in 2020 to 9 in 2025.

Which Engineering Mathematics topics repeat most in GATE CS?

By the number of years they appeared in: Linear Algebra, Calculus, Probability. The concept table on this page lists every concept with its question count and years.

Are these the official GATE CS Engineering Mathematics questions?

Yes. Each question comes from the official GATE CS question paper for that year, and the key, marks and question type come from the official answer key. Summaries are ours; open the official PDF for the full question.

What question types does Engineering Mathematics use in GATE CS?

Of 55 questions: 19 MCQ, 8 MSQ and 28 NAT. MSQ only appears from 2021 onwards. 24 of the 55 questions carry 2 marks.