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.

GATE Engineering Mathematics (Linear Algebra): For a $3 \times 3$ real matrix $A$ in 'Linear Algebra: Matrices, Determinants, Rank, Eigenvalues and Cayley-Hamilton Theorem' with eigenvalues $\lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 3$, what is the determinant $\det(A)$?

(A)

$6$ ($\det(A) = \lambda_1 \lambda_2 \lambda_3 = 1 \times 2 \times 3 = 6$) (Linear Algebra: Matrices, Determinants, Rank, Eigenvalues and Cayley-Hamilton Theorem)

(B)

$0$

(C)

$14$

(D)

$1$

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Q2.

Calculus: Evaluate the limit $\lim_{x \to 0} \frac{\sin x - x}{x^3}$ in 'Linear Algebra: Matrices, Determinants, Rank, Eigenvalues and Cayley-Hamilton Theorem':

(A)

$-\frac{1}{6}$ (Using Taylor expansion $\sin x = x - \frac{x^3}{6} + \dots$) (Linear Algebra: Matrices, Determinants, Rank, Eigenvalues and Cayley-Hamilton Theorem)

(B)

$0$

(C)

$\frac{{1}}{{6}}$

(D)

$1$

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