60 solved GATE CS questions on Engineering Mathematics, drawn from 3 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.
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State the domain, continuity, or convergence condition a formula requires before substituting. These selected foundations connect calculus, linear algebra, probability, and discrete mathematics as they appear in the GATE CS syllabus. Each topic needs its own deeper study.
Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.
A proposition has a fixed truth value. p → q is false only when p is true and q is false; it is vacuously true when p is false. Predicate logic quantifies over a domain: ∀x P(x) fails if any element violates P; ∃x P(x) succeeds if any element satisfies P.
Check yourself: Have you checked the implication when the antecedent is false?
C(n, k) = n!/(k!(n−k)!) counts selections without order. Recurrences define sequences through prior terms. Solve by finding a closed-form solution that satisfies both the recurrence and initial conditions. The Master Theorem applies to specific divide-and-conquer forms.
Check yourself: Does your base case produce the correct initial value?
A function is continuous at a point when its limit equals its value. A definite integral computes net signed area. Integration by parts and substitution require matching differentials. Verify convergence before evaluating an improper integral.
Check yourself: Is the integrand defined and continuous on the interval, including endpoints?
A simple graph with n vertices and m edges satisfies the handshaking lemma: the degree sum equals 2m. A tree on n vertices has exactly n − 1 edges. An Euler circuit exists when every vertex has even degree and the graph is connected. Distinguish paths, walks, and circuits.
Check yourself: Are you counting edges or vertices, and is the graph connected?
For equally likely outcomes, probability is favorable/total. Use conditional probability P(A|B) = P(A ∩ B)/P(B) and distinguish independence from mutual exclusivity. Expected value is linear: E(X + Y) = E(X) + E(Y) regardless of dependence.
Check yourself: Are the outcomes truly equally likely under your counting?
Original teaching example · not a PYQ
Original mini-example: a connected simple graph has 6 vertices. Every vertex has degree 2. How many edges does it have, and does it admit an Euler circuit?
6 edges; yes, an Euler circuit exists.
How many distinct ways can you choose 3 items from a set of 5 when order does not matter?
C(5, 3) = 10.
C(5, 3) = 5!/(3! × 2!) = 120/(6 × 2) = 10. The permutation count P(5, 3) = 60 would overcount by 3! = 6 because it distinguishes order.
Supplemental reading, not an official GATE reading list or an endorsement of these notes.
Free supplemental lecture notes, problem sets, and solutions covering logic, graph theory, counting, and probability as used in computer science.
This page shows 60 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE CS papers. Questions can carry more than one subject tag; counts are not marks weightage.
G(V, E) be a simple, undirected graph. A vertex cover of is a subset such that for every , or .…MSQ · +2 marks · MediumG(V, E) is said to be 2-colorable if there exists a function such that for every…MSQ · +2 marks · MediumContinue learning with Success Tracker
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