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GATE CS Engineering Mathematics questions

Practise Engineering Mathematics questions for GATE CS. Explore official PYQs and original subject-wise quizzes, check answers and view available solutions. Free, no sign-in.

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Official PYQ1994Engineering MathematicsGraphs: Connectivity, Matching, ColouringMCQ · 1 mark
The number of distinct simple graphs with up to three nodes is
Official PYQ1994Engineering MathematicsConditional Probability and Bayes TheoremMCQ · 1 mark
Let AA and BB be any two arbitrary events, then, which one of the following is TRUE?
Official PYQ1994Engineering MathematicsLinear Algebra: Matrices, Determinants, System of Linear EquationsMCQ · 1 mark
Let AA and BB be real symmetric matrices of size n×nn \times n. Then which one of the following is true?
Official PYQ1993Engineering MathematicsPartial Orders and LatticesMCQ · 1 mark
The less-than relation, <,<, on real number is
Official PYQ1993Engineering MathematicsSets, Relations and FunctionsMCQ · 1 mark
Let AA and BB be sets with cardinalities mm and nn respectively. The number of one-one mappings from AA to BB, when m<nm < n, is
Official PYQ1993Engineering MathematicsPropositional and First Order LogicMCQ · 1 mark
Let A be a finite set of size n. The number of elements in the power set of A×AA\times A is:
Official PYQ1993Engineering MathematicsPropositional and First Order LogicMCQ · 1 mark
The proposition p∧(∼p∨q)p \wedge (\sim p \vee q) is:
Official PYQ1993Engineering MathematicsSets, Relations and FunctionsMCQ · 1 mark
Let SS be an infinite set and S1…,SnS_1 \dots , S_n be sets such that S1∪S2∪⋯∪Sn=SS_1 \cup S_2 \cup \dots \cup S_n = S. Then
Official PYQ1993Engineering MathematicsGraphs: Connectivity, Matching, ColouringMSQ · 1 mark
Consider a simple connected graph GG with nn vertices and nn edges (n>2)(n > 2). Then, which of the following statements are true?
Official PYQ1993Engineering MathematicsCalculus: Limits, Continuity, DifferentiabilityNAT · 1 mark
lim⁡x→0x(ex−1)+2(cos⁡x−1)x(1−cos⁡x)\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)} is __________
Official PYQ1993Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
The function f(x,y)=x2y−3xy+2y+xf\left(x,y\right) = x^2y - 3xy + 2y +x has
Official PYQ1993Engineering MathematicsMaxima and Minima, Mean Value Theorem, IntegrationMCQ · 1 mark
Which of the following improper integrals is (are) convergent?
Official PYQ1993Engineering MathematicsCalculus: Limits, Continuity, DifferentiabilityMCQ · 1 mark
The differential equation d2ydx2+dydx+sin⁡y=0\frac{d^2 y}{dx^2}+\frac{dy}{dx}+\sin y =0 is:
Official PYQ1993Engineering MathematicsCalculus: Limits, Continuity, DifferentiabilityMCQ · 1 mark
Fourier series of the periodic function (period 2π) defined by f(x)={0,−p<x<0x,0<x<p is π4+∑[1πn2(cos⁡nπ−1)cos⁡nx−1ncos⁡nπsin⁡nx]f(x) = \begin{cases} 0, -p < x < 0\\x, 0 < x < p \end{cases} \text{ is }\\ \frac{\pi}{4} + \sum \left [ \frac{1}{\pi n^2} \left(\cos n\pi - 1 \right) \cos nx - \frac{1}{n} \cos n\pi \sin nx \right ] But putting x=πx = \pi, we get the sum of the series …
Official PYQ1993Engineering MathematicsEigenvalues and Eigenvectors, LU DecompositionMSQ · 1 mark
The eigen vector (s)(s) of the matrix [00α000000],α≠0\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0 is (are)
Official PYQ1992Engineering MathematicsPartial Orders and LatticesMCQ · 1 mark
Consider the set of integers {1,2,3,4,6,8,12,24}\{1,2,3,4,6,8,12,24\} together with the two binary operations LCM (lowest common multiple) and GCD (greatest common divisor). Which of the following algebraic structures does this represent?
Official PYQ1992Engineering MathematicsPropositional and First Order LogicMCQ · 1 mark
Which of the following is/are a tautology?
Official PYQ1992Engineering MathematicsGraphs: Connectivity, Matching, ColouringMCQ · 1 mark
A non-planar graph with minimum number of vertices has
Official PYQ1992Engineering MathematicsPropositional and First Order LogicMCQ · 1 mark
Which of the following predicate calculus statements is/are valid?
Official PYQ1991Engineering MathematicsPropositional and First Order LogicMCQ · 1 mark
If F1F_1, F2F_2 and F3F_3 are propositional formulae such that F1∧F2→F3F_1 \land F_2 \rightarrow F_3 and F1∧F2→∼F3F_1 \land F_2 \rightarrow \sim F_3 are both tautologies, then which of the following is true: