NDA MATHEMATICS QUIZ-7

Question 1:

It $\vec{a}, \bar{b}, \vec{c}$ be three vectors satisfing $\vec{a}+\bar{b}+\vec{c}$ $=0$ where $|\bar{a}|=|\bar{b}|=|\vec{c}|=1$ then the angle between $\bar{b}$ and $\vec{c}$ is

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{2 \pi}{3}$

Question 2:

Solution of the differential equation $x^{2}\frac{d y}{d x}+(1-2 x) y=x^{2}$ will be

$y=x^{2}\left(1+c e^{-1 / x}\right)$

$y=x^{2}\left(1-c e^{-x^{2}}\right)$

$y=x^{2}\left(1+c e^{-\frac{1}{x^{2}}}\right)$

$y=x c\left(1+e^{-\frac{1}{x}}\right)$

Question 3:

$\int \frac{x d x}{(x+2) \sqrt{x+1}}$ is equal to:

$2 \sqrt{x+1}-4 \tan^ {-1} \sqrt{x+1}+c$

$\sqrt{x+1}-2 \tan ^{-1} \sqrt{x+1}+c$

$3 \tan ^{-1} \sqrt{x+1}-4 \sqrt{x+1}+c$

$\tan ^{-1} \sqrt{x+1}-2 \sqrt{x+1}+c$

Question 4:

The number of integral points at which the function $f(x)=\frac{1}{\log \left|\left(x^{2}-1\right)\right|}$ is discontinuous is:

2.0

3.0

4.0

5.0

Question 5:

If $\alpha \neq \beta$ but $x^2=8 x-15$, then the equation with roots $\frac{\alpha}{\beta}, \frac{\beta}{\alpha}$ is:

$3 x^2-25 x+3=0$

$9x^2+27 x-15=0$

$14x^2-25 x+3=0$

$ 15 x^2-34 x+15=0$

Question 6:

The Number of ways it which 6 beads of different colors to form a necklace is

60.0

120.0

90.0

100.0

Question 7:

From which point the tangents to ellipse $9 x^{2}+16 y^{2}=144$ are perpendicular?

$\left(\frac{5}{\sqrt{2}}, \frac{5}{\sqrt{2}}\right)$

$(5 \sqrt{3}, 5 \sqrt{2})$

$\left(\frac{5}{\sqrt{3}}, \frac{5}{\sqrt{3}}\right)$

$\left(\frac{5}{\sqrt{3}}, \frac{5}{\sqrt{2}}\right)$

Question 8:

In a class of 20 students a foot ball team of 11 players is to be selected. number of selections when a particular student is always left will be.

$19_{C_{11}}$

$20_{C_{10}}$

$18_{C_{11}}$

$20_{C_{9}}$

Question 9:

If the line of shortest distance between two lines passing through respectively $\left(\alpha_{1}, \beta_{1},\gamma_{1}\right)$ and $\left(\alpha_{2}, \beta_{2},\gamma_{2}\right)$ is having $l, m, n$ as the direction cosines then the length of shortest distance between the lines will be

$l\left(\alpha_{2}-\alpha_{1}\right)+m\left(\beta_{2}-\beta_{1}\right)+n\left(\gamma_{2}-\gamma_{1}\right)$

$l^{2}\left(\alpha_{2}-\alpha_{1}\right)^{2}+m^{2}\left(\beta_{2}-\beta_{1}\right)^{2}+n^{2}\left(\gamma_{2}-\gamma_{1}\right)^{2}$

$\operatorname{mn}\left(\alpha_{2}-\alpha_{1}\right)+ln \left(\beta_{2}-\beta_{1}\right)+\operatorname{mn}\left(\gamma_{2}-\gamma_{1}\right)$

$l\left(\alpha_{2}-\alpha_{1}\right)^{2}+m\left(\beta_{2}-\beta_{1}\right)^{2}+n\left(\gamma_{2}-\gamma_{1}\right)^{2}$

Question 10:

If $\cos ^{-1} \frac{\alpha}{2}+\cos ^{-1} \frac{\beta}{3}=x$ then value of $9 \alpha^{2}-12 \alpha \beta \cos x+4 \beta^{2}$ is.

$36 \sin ^{2} x$

$24 \sin ^{2} x$

$48 \cos ^{2} x$

$72 \cos ^{2} x$