# NDA MATHEMATICS QUIZ

Attempt now to get your rank among 49 students!

## Question 1:

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

## Question 2:

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

## Question 3:

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

## Question 4:

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

## 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 $\mathrm{f}^{\prime}(0)$

## Question 6:

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

## 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.

## Question 8:

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

## Question 9:

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

## 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.