GATE Engineering - General Aptitude & Engineering Mathematics

Verbal Ability, Quantitative & Spatial Aptitude question bank (General Aptitude (Verbal & Numerical Ability))

Practice 24 free GATE Engineering - General Aptitude & Engineering Mathematics General Aptitude (Verbal & Numerical Ability) - Verbal Ability, Quantitative & Spatial Aptitude 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 'Verbal Aptitude: English Grammar, Sentence Completion and Verbal Deductions' with eigenvalues $\lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 3$, what is the determinant $\det(A)$?

(A)

$6$ ($\det(A) = \lambda_1 \lambda_2 \lambda_3 = 1 \times 2 \times 3 = 6$) (Verbal Aptitude: English Grammar, Sentence Completion and Verbal Deductions)

(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 'Verbal Aptitude: English Grammar, Sentence Completion and Verbal Deductions':

(A)

$-\frac{1}{6}$ (Using Taylor expansion $\sin x = x - \frac{x^3}{6} + \dots$) (Verbal Aptitude: English Grammar, Sentence Completion and Verbal Deductions)

(B)

$0$

(C)

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

(D)

$1$

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