Defence Exams - NDA Mathematics (Paper 1)

Applied Advanced Mathematics & Analysis question bank (Calculus, Vectors, Probability & Statistics)

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Q1.

3D Geometry: In '3D Geometry: Direction Cosines, Direction Ratios, Planes and Lines in Space', what is the acute angle between the two planes $2x - y + z = 6$ and $x + y + 2z = 7$?

(A)

$\frac{\pi}{3}$ or $60^\circ$ ($\cos \theta = \frac{|2(1) + (-1)(1) + 1(2)|}{\sqrt{4+1+1}\sqrt{1+1+4}} = \frac{3}{6} = \frac{1}{2}$) (3D Geometry: Direction Cosines, Direction Ratios, Planes and Lines in Space)

(B)

$\frac{{\pi}}{{4}}$ or $45^\circ$

(C)

$\frac{{\pi}}{{6}}$ or $30^\circ$

(D)

$\frac{{\pi}}{{2}}$ or $90^\circ$

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Q2.

Probability & Bayes' Theorem: A missile guidance system in '3D Geometry: Direction Cosines, Direction Ratios, Planes and Lines in Space' has two tracking radars $R_1$ and $R_2$ detecting targets with probabilities $0.8$ and $0.7$ independently. What is the probability that at least one radar detects the target?

(A)

$0.94$ ($1 - P(R_1' \cap R_2') = 1 - (0.2 \times 0.3) = 1 - 0.06$) (3D Geometry: Direction Cosines, Direction Ratios, Planes and Lines in Space)

(B)

$0.56$

(C)

$0.85$

(D)

$0.76$

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