NDA MATHEMATICS QUIZ

Question 1:

Total number of terms in the expansion of $(a+1)^{200}+(1-a)^{200}$ is:

100.0

201.0

101.0

200.0

Question 2:

$\tan ^{-1}\left(\frac{\cos \theta}{1+\sin \theta}\right)=\ldots . . ;-\frac{\pi}{2} \leq \theta \leq \frac{3 \pi}{2}$

$\frac{\pi}{4}+\frac{\theta}{2}$

$\frac{\pi}{4}+\frac{\theta}{4}$

$\frac{\pi}{4}-\frac{\theta}{4}$

$\frac{\pi}{4}-\frac{\theta}{2}$

Question 3:

Value of $\cot \left(\sin ^{-1} \frac{3}{5}+\cot ^{-1} \frac{3}{2}\right)$ is

$\frac{11}{17}$

$\frac{1}{17}$

$\frac{5}{17}$

$\frac{6}{17}$

Question 4:

If $\sqrt{1-x^{2}}+\sqrt{1-y^{2}}=\alpha(x-y)$ then $\frac{d y}{d x}$ is:

$\left(\sqrt{1-y^{2}}\right)\left(\sqrt{1-x^{2}}\right)$

$-\frac{\sqrt{1-y^{2}}}{\sqrt{1-x^{2}}}$

$\frac{\sqrt{1-y^{2}}}{\sqrt{1-x^{2}}}$

$\frac{\sqrt{1+x^{2}}}{\sqrt{1-y^{2}}}$

Question 5:

The function defined by $f(x)=\frac{3 x}{\frac{2}{x}}+1+2 \mathrm{c}$, when $x \neq 0=0, x=0$ then $\mathrm{f}^{\prime}(0)$

Exists

is equal to 0

is equal to 1

does not create

Question 6:

$\int_{0}^{1} \frac{\tan ^{-1} x \cdot e^{\tan ^{-1} x}}{\left(1+x^{2}\right)} $ is equals.

$\frac{\pi}{4}\left(e^{\frac{\pi}{4}}\right)-e^{\frac{\pi}{4}}+1$

$\frac{\pi}{4}-e^{\pi / 4{}}$

$\frac{\pi}{4} e^{\frac{\pi}{4}}$

$\left(\frac{\pi}{4}-2 e^{\pi / 4}-1\right)$

Question 7:

The equation $a x^{2}+2 h x y+b y^{2}+2 g x+2 b y+c=0$ represents a pair of parallel straight lines if.

$a f^{2}=b g^{2}$

af $^{2}=b^{2} g^{2}$

$a f=b g$

$a^{2} f^{2}=b g^{2}$

Question 8:

If $\cos A+\cos C=4 \sin ^{2} \frac{B}{2}$ then sides of the triangle are in

A.P.

G.P.

H.P.

None of these

Question 9:

The Number of proper subsets of the set A = $\{p, q, r, s\}$ will be -

16.0

15.0

8.0

17.0

Question 10:

If $X=\left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right]$ and $X^{2}-k X-I_{2}=0$

then $k$ equals.

4.0

5.0

2.0

3.0