NDA MATHEMATICS QUIZ

Question 1:

In a class of 80 students 40 students take Tea, 16 students take Coffee, , 11 students take cold drinks while 8 students take both Tea and Coffee , 6 students take Coffee and cold drinks, 2 students take tea and cold drinks, one student took all the three beverages. Then the number of students who did not take any of the beverages is -

52

40

28

36

Question 2:

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 3:

The number of solutions of the equation $\sin ^{-1} x+\sin ^{-1} 2 x=\frac{\pi}{3}$ is

4.0

2.0

1.0

3.0

Question 4:

If $\tan x, \cos x$ and $\sin x$ are in G.P. then value of $\cot ^{6} x-\cot ^{2} x$ is equal to

0.0

1.0

2.0

3.0

Question 5:

If $\alpha+\beta+\gamma=\pi$ and $\cos \alpha=\cos \beta \cdot \cos \gamma$ , then $\cot \beta \cdot \cot \gamma$ equal is

2

$\frac{1}{2}$

1

$\frac{1}{3}$

Question 6:

$\int_{0}^{\pi} \frac{x d x}{a^{2} \cos ^{2} x+b^{2} \sin ^{2} x}=\ldots \ldots \ldots ?$

$\frac{\pi}{2 a b}$

$\frac{\pi^{2}}{a b}$

$\frac{\pi^{2}}{2 a b}$

$\frac{\pi}{a b}$

Question 7:

If $x^{y}=\mathrm{e}^{x-y}$ then $\frac{d y}{d x}=\ldots \ldots$

$-\frac{\log x}{(1+\log x)^{2}}$

$-\frac{1}{(1+\log x)^{2}}$

$\frac{\log x}{(1+\log x)^{2}}$

$\frac{x}{(1+\log x)^{2}}$

Question 8:

If $y=e^{\operatorname{ax}} \sin b x$ then $\frac{d^{2} y}{d x^{2}}-2 x \frac{d y}{d x}+k g=0$ where $\mathrm{k}$ equals:

$2\left(\mathrm{a}^{2}-\mathrm{b}^{2}\right)$

$\left(a^{2}+b^{2}\right)^{2}$

$2 \mathrm{ab}$

$a^{2}+b^{2}$

Question 9:

$\operatorname{Lt}_{x \rightarrow 2} \frac{x-2}{\sqrt{x^{2}-4}+\sqrt{x-2}}=$

1.0

0.0

2.0

3.0

Question 10:

$\operatorname{Lt}_{x \rightarrow 0} \frac{x. 2^{x}-x}{1-\cos x}=\ldots$

$3 \log 2$

$2 \log 2$

$\log 6$

$2 \log 3$