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GATE CS question library

Practise GATE CS Computer Science previous year questions free. Browse by subject, syllabus topic, year and question type, with answers and available solutions.

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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 PYQ1993Numerical Methods (Historical)MSQ · 1 mark
Simpson's rule for integration gives exact result when f(x)f(x) is a polynomial of degree