GATE Engineering - General Aptitude & Engineering Mathematics

Linear Algebra, Calculus, Differential Equations & Probability question bank (Engineering Mathematics)

Practice 40 free GATE Engineering - General Aptitude & Engineering Mathematics Engineering Mathematics - Linear Algebra, Calculus, Differential Equations & Probability questions with answers and step-by-step solutions.

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Q1.

Differential Equations: In 'Linear Algebra: Matrices, Determinants, Rank, Eigenvalues and Cayley-Hamilton Theorem', what is the integrating factor of the linear differential equation $\frac{dy}{dx} + \left(\frac{2}{x}\right)y = x^3$ (for $x > 0$)?

(A)

$x^2$ ($I.F. = e^{\int (2/x) dx} = e^{2 \ln x} = x^2$) (Linear Algebra: Matrices, Determinants, Rank, Eigenvalues and Cayley-Hamilton Theorem)

(B)

$x$

(C)

$\ln x$

(D)

$e^{{2x}}$

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Q2.

Probability & Statistics: In a Poisson process in 'Linear Algebra: Matrices, Determinants, Rank, Eigenvalues and Cayley-Hamilton Theorem' with arrival rate $\lambda = 2$ events per hour, what is the probability of observing exactly 0 events in an hour?

(A)

$e^{-2} \approx 0.1353$ ($P(X=0) = \frac{\lambda^0 e^{-\lambda}}{0!} = e^{-2}$) (Linear Algebra: Matrices, Determinants, Rank, Eigenvalues and Cayley-Hamilton Theorem)

(B)

$1 - e^{{-2}}$

(C)

$2e^{{-2}}$

(D)

$0.5$

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