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

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

Answer first

Discrete Mathematics has appeared in 11 of the 11 official GATE CS papers from 2016–2026, with 61 questions in all. It averages 8.6 marks a year, which puts it 3rd of 11 technical subjects. The last three papers gave it 7 (2026), 8 (2025), 6 (2024).

The concepts that came back most often are Graph Theory, Combinatorics, Sets, Relations & Functions. Graph Theory, Combinatorics, Sets, Relations & Functions appeared in at least 7 of the 11 years. 39% 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 Discrete 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 Discrete 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.12 · 1 mark · MCQ · Combinatorics: Count 0/1 4×4 matrices with even 1s in every row and column (key: A)
• Q.47 · 2 marks · MSQ · Graph Theory: Conditions that force a vertex into every minimum vertex cover (key: A)
• Q.55 · 2 marks · MSQ · Graph Theory: Properties of 2-colourable (bipartite) graphs (key: B, C)
• Q.57 · 2 marks · NAT · Combinatorics: Number of matchings in a path on 8 vertices (key: 34)

Paper: official PDF · GATE CS 2026 page

GATE CS 2025 (CS1)

• Q.17 · 1 mark · MCQ · Sets, Relations & Functions: What follows about g when f and f composed with g are onto (key: D)
• Q.30 · 1 mark · NAT · Combinatorics: Count length-5 ternary strings with two equal adjacent symbols (key: 195)
• Q.43 · 2 marks · MCQ · Graph Theory: Bounds involving the diameter of a 100-vertex graph (key: C)
• Q.48 · 2 marks · MSQ · First-Order Logic: Predicate formulas expressing that everyone has exactly one mother (key: B, D)
• Q.49 · 2 marks · MSQ · Algebraic Structures: Algebraic properties of pointwise addition of functions (key: B)

Paper: official PDF · GATE CS 2025 page

GATE CS 2024 (CS1)

• Q.32 · 1 mark · NAT · Sets, Relations & Functions: Possible sizes of a set given bijections involving products and unions (key: 2)
• Q.34 · 1 mark · NAT · Graph Theory: Number of spanning trees of the complete graph on four vertices (key: 16)
• Q.51 · 2 marks · MSQ · Graph Theory: Statements implied by a graph's chromatic number (key: B, C)
• Q.52 · 2 marks · MSQ · Algebraic Structures: Associativity and commutativity of two custom operators (key: B, D)

Paper: official PDF · GATE CS 2024 page

GATE CS 2023

• Q.15 · 1 mark · MCQ · Recurrences: Closed form of the Lucas sequence recurrence (key: A)
• Q.26 · 1 mark · MSQ · First-Order Logic: Which quantified statements imply a given conjecture about integers (key: B, C)
• Q.48 · 2 marks · MCQ · Combinatorics: Number of permutations that separate two disjoint subsets (key: D)
• Q.49 · 2 marks · MSQ · Sets, Relations & Functions: Properties of equivalence classes induced by an onto function (key: B, C, D)
• Q.51 · 2 marks · MSQ · Group Theory: Whether the power set with symmetric difference forms a group (key: A, D)
• Q.55 · 2 marks · MSQ · Graph Theory: Bounds on colours used by greedy vertex colouring (key: A, B)
• Q.56 · 2 marks · NAT · Combinatorics: Number of orderings of power-set vertices along chains in a graph (key: 5040)

Paper: official PDF · GATE CS 2023 page

GATE CS 2022

• Q.27 · 1 mark · MSQ · Group Theory: Conditions under which a group must be commutative (key: A,B,C)
• Q.30 · 1 mark · NAT · Graph Theory: Maximum edges in a disconnected simple graph on 10 vertices (key: 36)
• Q.32 · 1 mark · NAT · Combinatorics: Ways to place six identical balls into three identical bins (key: 7)
• Q.36 · 2 marks · MCQ · Generating Functions: Closed form of the generating function of an alternating sequence (key: A)
• Q.37 · 2 marks · MCQ · Graph Theory: Count of 3-cycles in a graph from the trace of the cubed adjacency matrix (key: D)
• Q.50 · 2 marks · MSQ · Graph Theory: Properties of the Petersen graph: colouring, Hamiltonian path, isomorphism (key: A,B,C)
• Q.51 · 2 marks · MSQ · Recurrences: Closed-form values of a recurrence defined on even and odd arguments (key: A,B,C)
• Q.52 · 2 marks · MSQ · Graph Theory: Properties of powers of an adjacency matrix of a simple graph (key: A)

Paper: official PDF · GATE CS 2022 page

GATE CS 2021 (set 1)

• Q.7 · 1 mark · MCQ · Propositional Logic: Which of two propositional formulas are tautologies (key: B)
• Q.16 · 1 mark · NAT · Graph Theory: Edge count of a planar graph from vertices and faces (key: 11)
• Q.19 · 1 mark · NAT · Combinatorics: Ways to assign six jobs to three computers under constraints (key: 65)
• Q.34 · 2 marks · MCQ · Group Theory: Cyclicity of a group of order 6 and its proper subgroups (key: B)
• Q.36 · 2 marks · MCQ · Graph Theory: Diameter of a graph built from the square of an adjacency matrix (key: A)
• Q.43 · 2 marks · MSQ · Sets, Relations & Functions: Circular relations and equivalence relations (key: C)

Paper: official PDF · GATE CS 2021 page

GATE CS 2020

• Q.17 · 1 mark · NAT · Sets, Relations & Functions: Probability a random relation on {1,2,3} is reflexive (key: 0.125)
• Q.18 · 1 mark · NAT · Group Theory: Largest proper subgroup size of a group of order 35 (key: 7)
• Q.39 · 2 marks · MCQ · First-Order Logic: Identify the quantified formula that is not valid (key: C)
• Q.42 · 2 marks · NAT · Combinatorics: Derangements of the letters of LILAC with repeated L (key: 12)
• Q.52 · 2 marks · NAT · Graph Theory: Edge chromatic number of a wheel-like graph (key: 7)

Paper: official PDF · GATE CS 2020 page

GATE CS 2019

• Q.5 · 1 mark · MCQ · Combinatorics: Count pairs of an element and a subset containing it (key: C)
• Q.10 · 1 mark · MCQ · Group Theory: Which relations on a group are equivalence relations (key: B)
• Q.12 · 1 mark · MCQ · Graph Theory: Number of distinct Hamiltonian cycles in a complete graph (key: C or D)
• Q.21 · 1 mark · NAT · Number Theory: Compute a large power modulo 5 (key: 2)
• Q.35 · 2 marks · MCQ · First-Order Logic: Meaning of a first-order formula about primes (key: C)
• Q.48 · 2 marks · NAT · Group Theory: Count strings of permutations composing to the identity (key: 120)

Paper: official PDF · GATE CS 2019 page

GATE CS 2018

• Q.1 · 1 mark · MCQ · Generating Functions: Closed form of the generating function for 2n+3 (key: D)
• Q.18 · 1 mark · NAT · Graph Theory: Chromatic number of a given graph (key: 3)
• Q.19 · 1 mark · NAT · Group Theory: Largest proper subgroup of a group of order 84 (key: 42)
• Q.27 · 2 marks · MCQ · Sets, Relations & Functions: Which sets are countable (key: D)
• Q.28 · 2 marks · MCQ · First-Order Logic: Satisfiability of a first-order sentence over finite domains (key: A)
• Q.43 · 2 marks · NAT · Graph Theory: Vertex degree plus components in a graph of permutations under adjacent swaps (key: 109)

Paper: official PDF · GATE CS 2018 page

GATE CS 2017 (set 1)

• Q.1 · 1 mark · MCQ · Propositional Logic: Which formulas are equivalent to a given implication (key: D)
• Q.2 · 1 mark · MCQ · First-Order Logic: Which sentences are implied by a quantified first-order formula (key: B)
• Q.20 · 1 mark · NAT · Graph Theory: Sum of vertex degrees in a tree with 10 vertices (key: 18.0)
• Q.29 · 2 marks · MCQ · Propositional Logic: Nature of an expression given another is a contradiction (key: D)
• Q.47 · 2 marks · NAT · Combinatorics: Integers up to 500 divisible by 3, 5 or 7 (key: 271.0)

Paper: official PDF · GATE CS 2017 page

GATE CS 2016 (set 1)

• Q.1 · 1 mark · NAT · Propositional Logic: Find the integer satisfying a compound propositional formula (key: 11.0 : 11.0)
• Q.2 · 1 mark · MCQ · Recurrences: Recurrence for n-bit strings with no two consecutive 1s (key: B)
• Q.26 · 2 marks · NAT · Combinatorics: Coefficient of x^12 in a generating function power (key: 10.0 : 10.0)
• Q.27 · 2 marks · NAT · Recurrences: Solve a recurrence and evaluate its 99th term (key: 197.9 : 198.1)
• Q.28 · 2 marks · NAT · Sets, Relations & Functions: Number of distinct values of a recursively defined function (key: 2.0 : 2.0)

Paper: official PDF · GATE CS 2016 page

Other GATE CS subjects

• General Aptitude
• Engineering 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 Discrete Mathematics carry in GATE CS?

Across the official GATE CS papers from 2016–2026 (one set per year), Discrete Mathematics carried 8.6 marks a year on average, from 6 in 2024 to 13 in 2022.

Which Discrete Mathematics topics repeat most in GATE CS?

By the number of years they appeared in: Graph Theory, Combinatorics, Sets, Relations & Functions. The concept table on this page lists every concept with its question count and years.

Are these the official GATE CS Discrete 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 Discrete Mathematics use in GATE CS?

Of 61 questions: 22 MCQ, 15 MSQ and 24 NAT. MSQ only appears from 2021 onwards. 34 of the 61 questions carry 2 marks.