Defence Exams - NDA Mathematics (Paper 1)

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Q1.

UPSC NDA Mathematics (Complex Numbers / Algebra): In '3D Geometry: Direction Cosines, Direction Ratios, Planes and Lines in Space', what is the modulus and principal argument of the complex number $z = -1 + i\sqrt{3}$?

(A)

$|z| = 2$ and $\arg(z) = \frac{2\pi}{3}$ (in second quadrant) (3D Geometry: Direction Cosines, Direction Ratios, Planes and Lines in Space)

(B)

$|z| = 2$ and $\arg(z) = \frac{{\pi}}{{3}}$

(C)

$|z| = 4$ and $\arg(z) = \frac{{5\pi}}{{6}}$

(D)

$|z| = 1$ and $\arg(z) = \pi$

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Q2.

Matrices & Determinants: If $A$ is a non-singular square matrix of order $3 \times 3$ with $\det(A) = 5$ in '3D Geometry: Direction Cosines, Direction Ratios, Planes and Lines in Space', then $\det(\text{adj}(A))$ is equal to:

(A)

$25$ ($\det(\text{adj}(A)) = |A|^{n-1} = 5^{3-1} = 25$) (3D Geometry: Direction Cosines, Direction Ratios, Planes and Lines in Space)

(B)

$125$

(C)

$5$

(D)

$1/5$

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