Discrete Mathematics: notes and questions
For CSE/IT students
Notes for each topic, a formula sheet, practice questions and 45 past GATE questions from 10 papers (2018–2026), 45 of them solved step by step.
- previous-year questions
- 45previous-year questions
- solved step by step
- 45solved step by step
- GATE papers, 2018–2026
- 10GATE papers, 2018–2026
- topics with notes
- 6topics with notes
Foundation
Learn the subject one topic at a time. Each topic has notes, the key formulas and practice questions.
Topic notes and formulas
Notes on every topic, with the key formulas and practice.
Propositional and first-order logic
Propositional logic studies statements built from true/false atoms with connectives, and first-order logic adds predicates and the quantifiers and over a domain.
5 practice questions
Sets, relations, functions, partial orders and lattices
This topic covers sets, relations, functions, partial orders and lattices, the vocabulary used all through discrete mathematics.
6 practice questions
Monoids and groups
A group is a set with one associative operation that has an identity and gives every element an inverse.
6 practice questions
Graph theory: connectivity, matching and colouring
Graph theory studies vertices and edges and the structure they force: how many edges a graph can have, when it is connected and how strongly, when vertices can be paired off (matching), how many colours a proper colouring needs, and when it can be drawn without crossings.
6 practice questions
Combinatorics: counting
Counting is the art of finding how many objects have a given property without listing them: choosing, arranging, distributing and avoiding forbidden cases.
6 practice questions
Recurrence relations and generating functions
A recurrence relation defines each term of a sequence from earlier terms, and a generating function packs a whole sequence into one power series.
5 practice questions
Discrete Mathematics formulas by topic
GATE
Past GATE questions on Discrete Mathematics by topic and year, the full papers, practice and the GATE syllabus.
45 questions, by topic and year
How many questions each topic had in the CS papers of each year. This shows what was asked, not what will be asked. We placed each question under a topic ourselves; the exam paper does not label topics.
| Topic | 2018 | 2020 | 2022 | 2023 | 2024 | 2025 | 2026 | Total |
|---|---|---|---|---|---|---|---|---|
| Mathematical logic | 1 | 1 | · | 1 | 1 | 2 | 1 | 7 |
| Sets & relations | 1 | 1 | · | 1 | 2 | 2 | 1 | 8 |
| Groups | 1 | 1 | 1 | 1 | 2 | 1 | · | 7 |
| Graph theory | 2 | 1 | 5 | · | 4 | · | 2 | 14 |
| Counting | · | 1 | 1 | 1 | · | 2 | 1 | 6 |
| Recurrences | 1 | · | 1 | 1 | · | · | · | 3 |
Solved papers
GATE CSE question papers with solutions: 2026 Set 1, 2026 Set 2, 2025 Set 1, 2025 Set 2, 2024 Set 1, 2024 Set 2, 2023, 2022, 2020, 2018
GATE 2023 comes from IIT Kanpur's own copy of the paper and its answer key, which numbers the CS questions Q.11 to Q.65. For 2024, 2025 and 2026 both sessions (CS1 and CS2) are included.
34 practice questions
The GATE syllabus for Discrete Mathematics, paper by paper
From the GATE 2027 syllabus PDF: the Discrete Mathematics part of CS Section 1, “Engineering Mathematics”. The rest of that section (linear algebra, calculus, and probability and statistics) is on the Engineering Mathematics page.
Show the GATE CS wordingHide the GATE CS wording
Discrete Mathematics: Propositional and first order logic. Sets, relations, functions, partial orders and lattices. Monoids, Groups. Graphs: connectivity, matching, colouring. Combinatorics: counting, recurrence relations, generating functions.
Preparing in Kolkata? See IAE Academy’s GATE CS coaching.
Other exams
6 questions on Discrete Mathematics from ISRO's Scientist/Engineer written test (ISRO CS 2025, ISRO CS 2023), by topic. They are not counted in the GATE numbers on this page.
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