NDA MATHEMATICS QUIZ-2

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Question 1:

In the polynomial $(α - 1) (α - 2) (α - 3) \dots . . (α - 100)$ . The coefficient of $α^{99}$ is:

बहुपद $(α - 1) (α - 2) (α - 3) \dots . (α - 100)$ में $α^{99}$ का गुणांक क्या होगा ?

5051.0

- 5055

- 5055

- 5050

- 5050

5000.0

Question 2:

$Let A = [\begin{array}{cc} \cos \frac{π}{4} & - \sin \frac{π}{4} \\ \sin \frac{π}{4} & \cos \frac{π}{4} \end{array}]$ and $X = [\begin{matrix} \frac{1}{\sqrt{2}} \\ \frac{1}{2} \end{matrix}]$ then $A^{3} X$ is equal to

माना A = $[\begin{array}{cc} \cos \frac{π}{4} & - \sin \frac{π}{4} \\ \sin \frac{π}{4} & \cos \frac{π}{4} \end{array}]$ और $X = [\begin{matrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{matrix}]$ तब $A^{3} X$ का मान कौन सा होगा ?

[\begin{array}{r} - 1 \\ 0 \end{array}]

[\begin{array}{r} - 1 \\ 0 \end{array}]

[\begin{matrix} - 1 \\ 1 \end{matrix}]

[\begin{matrix} - 1 \\ 1 \end{matrix}]

[\begin{matrix} - \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{matrix}]

[\begin{matrix} - \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{matrix}]

[\begin{matrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{matrix}]

[\begin{matrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{matrix}]

Question 3:

If X = {a,b,c,d}, Y = {b,d,f} then the number of elements of set Z satisfying X $\cap$ Y $\subseteq$ Z $\subseteq$ X $\cup$ Y is:

यदि X = {a,b,c,d}, Y = {b,d,f} तो समुच्च Z में अवयव की संख्या क्या होगी यदि X $\cap$ Y $\subseteq$ Z $\subseteq$ X $\cup$ Y है :

Question 4:

In a triangle $\frac{2 \cos A}{a} + \frac{\cos B}{b} + \frac{2 \cos C}{c}$ $= \frac{a}{b c} + \frac{b}{a c}$ then the value of angle $A$ is

यदि एक त्रिभुज ABC में $\frac{2 \cos A}{a} + \frac{\cos B}{b} + \frac{2 \cos C}{c} =$ $f r a c a b c + \frac{b}{a c}$ तो कोण A का मान क्या होगा ?

60^{\circ}

60^{\circ}

90^{\circ}

90^{\circ}

45^{\circ}

45^{\circ}

30^{\circ}

30^{\circ}

Question 5:

If $r^{2} = x^{2} + y^{2} + z^{2}$ then $\tan^{- 1} (\frac{y z}{x r}) + \tan^{- 1} (\frac{x z}{y r}) + \tan^{- 1} (\frac{x y}{z r})$ equals

यदि $r^{2} = x^{2} + y^{2} + z^{2}$ तो $\tan^{- 1} (\frac{y z}{x r}) + \tan^{- 1} (\frac{x z}{y r}) + \tan^{- 1} (\frac{x y}{z r})$ किसके बराबर होगा ?

\frac{π}{2}

\frac{π}{2}

\frac{π}{4}

\frac{π}{4}

\frac{π}{3}

\frac{π}{3}

π

π

Question 6:

The equation $\cos 2 θ + p \sin θ = 2 p - 7$ has a solution

समीकरण $\cos 2 θ + p \sin θ = 2 p - 7$ का एक हल है जबकि

2 \leq p \leq 6

2 \leq p \leq 6

p > 7

p > 7

p \leq 1

p \leq 1

0 \leq p \leq 1

0 \leq p \leq 1

Question 7:

$\int_{0}^{\frac{π}{2}} \frac{\sin^{\frac{3}{2}} x \cdot d x}{\cos^{\frac{3}{2}} x + \sin^{\frac{3}{2}} x} = \dots \dots$

\frac{π}{6}

\frac{π}{6}

π

π

\frac{π}{4}

\frac{π}{4}

\frac{π}{2}

\frac{π}{2}

Question 8:

If $y = \cos^{- 1} (\frac{x - x^{- 1}}{x + x^{- 1}})$ then $\frac{d y}{d x}$ will be:

यदि $y = \cos^{- 1} (\frac{x - x^{- 1}}{x + x^{- 1}})$ तो $\frac{d y}{d x}$ =

\frac{1}{1 + x^{2}}

\frac{1}{1 + x^{2}}

\frac{2}{1 + x^{2}}

\frac{2}{1 + x^{2}}

\frac{- 2}{1 + x^{2}}

\frac{- 2}{1 + x^{2}}

- \frac{1}{1 + x^{2}}

- \frac{1}{1 + x^{2}}

Question 9:

If $y = \sqrt{x} + \frac{1}{\sqrt{x}}$ then $2 x \frac{d y}{d x} + y$ is equal to

यदि $y = \sqrt{x} + \frac{1}{\sqrt{x}}$ तो $2 x \frac{d y}{d x} + y$ = . . . . . . . .

\sqrt{x}

\sqrt{x}

2 \sqrt{x}

2 \sqrt{x}

\frac{1}{2} \sqrt{x}

\frac{1}{2} \sqrt{x}

3 \sqrt{x}

3 \sqrt{x}

Question 10:

${Lt}_{x \to 0} \frac{x \cos x - \log (1 + x)}{x^{2}}$ equals:

${Lt}_{x \to 0} \frac{x \cos x - \log (1 + x)}{x^{2}}$ =

\frac{1}{3}

\frac{1}{3}

\frac{1}{4}

\frac{1}{4}

\frac{1}{2}

\frac{1}{2}

\frac{1}{6}

\frac{1}{6}