Defence Exams - NDA Mathematics (Paper 1)

Pure Mathematics for Defence Academy question bank (Algebra, Trigonometry & Coordinate Geometry)

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Q1.

Vector Algebra: In 'Sets, Venn Diagrams, Relations, Equivalence and Functions', what is the scalar projection of vector $\vec{a} = 2\hat{i} + 3\hat{j} + 2\hat{k}$ on the vector $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$?

(A)

$\frac{10}{\sqrt{6}}$ ($\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|} = \frac{2(1) + 3(2) + 2(1)}{\sqrt{1 + 4 + 1}}$) (Sets, Venn Diagrams, Relations, Equivalence and Functions)

(B)

$\frac{{8}}{{\sqrt{{6}}}}$

(C)

$\frac{{10}}{{6}}$

(D)

$10\sqrt{{6}}$

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Q2.

Definite Integrals: In 'Sets, Venn Diagrams, Relations, Equivalence and Functions', evaluate the integral $I = \int_{0}^{\pi/2} \frac{\sin^3 x}{\sin^3 x + \cos^3 x} \, dx$:

(A)

$\frac{\pi}{4}$ (Using property $\int_0^a f(x)dx = \int_0^a f(a-x)dx \implies 2I = \frac{\pi}{2}$) (Sets, Venn Diagrams, Relations, Equivalence and Functions)

(B)

$\frac{{\pi}}{{2}}$

(C)

$\frac{{\pi}}{{8}}$

(D)

$1$

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