NDA MATHEMATICS QUIZ

Question 1:

The function $y=x-\tan ^{-1} x$ decreases in the interval.

$(-\infty, 0)$

$(-1, \infty)$

$(-\infty, \infty)-(0)$

None of these

Question 2:

If the inverse of matrix $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & \lambda & 5\end{array}\right]$ exists then $\lambda$ must not be equal to.

2.0

3.0

1.0

4.0

Question 3:

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 4:

In certain locality of 900 people 480 persons read Hindi News paper and 320 persons read english News paper and 180 read both. Then the number of persons who read neither is -

280

240

320

180

Question 5:

In a triangle ABC , if $(s-b)(s-c)=s(s-a)$ then the angle $A$ is equal to

$60^{\circ}$

$90^{\circ}$

$45^{\circ}$

$30^{\circ}$

Question 6:

Area of a triangle ABC is given by $\Delta=\mathrm{b}^{2}$ $-(\mathrm{c}-\mathrm{a})^{2}$ then $\tan \frac{B}{2}$ is equal to

$\frac{1}{2}$

$\frac{1}{4}$

$-1$

$\frac{1}{3}$

Question 7:

If $\cot ^{-1} x+\operatorname{cosec}^{-1} \sqrt{5}=\frac{\pi}{4}$ then $x$ equals

2.0

1.0

3.0

$-1$

Question 8:

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 9:

$\int \frac{x d x}{x^{4}-x^{2}-2}=\ldots \ldots \ldots$

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

$\frac{1}{6} \log \frac{x^{2}-1}{x^{2}+2}$

$\frac{1}{6} \log \frac{x^{2}-2}{x^{2}+1}$

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

Question 10:

$\int \sin (\log x) \cdot d x=\ldots .$

$x[\sin (\log x)+\cos (\log x)]$

$\frac{x}{2}\{\sin (\log x)+\cos (\log x)\}$

$\frac{x}{2} \sin (\log x) \cdot \cos (\log x)$

$\frac{x}{2}\{\sin (\log x)-\cos (\log x)\}$