If A = $\left[\begin{array}{cc}2& 2\\ - 3& 2\end{array}\right], \mathrm{B} = \left[\begin{array}{cc}0& - 1\\ 1& 0\end{array}\right]$, then (B^{- 1}A^{- 1})^{- 1} is equal to

• $\left[\begin{array}{cc}2& - 2\\ 2& 3\end{array}\right]$

• $\left[\begin{array}{cc}2& 2\\ - 2& 3\end{array}\right]$

• $\left[\begin{array}{cc}2& - 3\\ 2& 2\end{array}\right]$

• $\left[\begin{array}{cc}1& - 1\\ - 2& 3\end{array}\right]$

If matrix A = $\left[\begin{array}{cc}1& 2\\ 4& 3\end{array}\right]$ such that AX = $\mathrm{\varphi }$,then X is equal to

• $\frac{1}{5}\left[\begin{array}{cc}1& 3\\ 2& - 1\end{array}\right]$

• $\frac{1}{5}\left[\begin{array}{cc}4& 2\\ 4& - 1\end{array}\right]$

• $\frac{1}{5}\left[\begin{array}{cc}- 3& 2\\ 4& - 1\end{array}\right]$

• $\frac{1}{5}\left[\begin{array}{cc}- 1& 2\\ - 1& 4\end{array}\right]$

13.

The differential equation of the family of circles touching Y-axis at the origin is

• $\left({\mathrm{x}}^2 + {\mathrm{y}}^2\right)\frac{\mathrm{dy}}{\mathrm{dx}} - 2\mathrm{xy} = 0$

• $\left({\mathrm{x}}^2 - {\mathrm{y}}^2\right) + 2\mathrm{xy}\frac{\mathrm{dy}}{\mathrm{dx}} = 0$

• $\left({\mathrm{x}}^2 - {\mathrm{y}}^2\right)\frac{\mathrm{dy}}{\mathrm{dx}} - 2\mathrm{xy} = 0$

• $\left({\mathrm{x}}^2 + {\mathrm{y}}^2\right)\frac{\mathrm{dy}}{\mathrm{dx}} + 2\mathrm{xy} = 0$

Direction cosines of the line $\frac{\mathrm{x} + 2}{2} = \frac{2\mathrm{y} - 5}{3}, \mathrm{z} = - 1$ are

• $\frac{4}{5}, \frac{3}{5}, 0$

• $\frac{3}{5}, \frac{4}{5}, \frac{1}{5}$

• $- \frac{3}{5}, \frac{4}{5}, 0$

• $\frac{4}{5}, - \frac{2}{5}, \frac{1}{5}$

$\int \frac{1}{\sqrt{8 + 2\mathrm{x} - {\mathrm{x}}^2}}\mathrm{dx}$ is equal to

• $\frac{1}{3}{\sin }^{-1}\left(\frac{\mathrm{x} - 1}{3}\right) + \mathrm{c}$

• ${\sin }^{-1}\left(\frac{\mathrm{x} + 1}{3}\right) + \mathrm{c}$

• $\frac{1}{3}{\sin }^{-1}\left(\frac{\mathrm{x} + 1}{3}\right) + \mathrm{c}$

• ${\sin }^{-1}\left(\frac{\mathrm{x} - 1}{3}\right) + \mathrm{c}$

If random variable waiting time in minutes for bus and probability density function of x is given by

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right) = \left\{\frac{1}{5}, 0 \le \mathrm{x} \le 5 \\ 0 , \mathrm{otherwise}\right\} \end{gathered}$$

then probability of waiting time not more than 4 minutes is equal to

• 0.3

• 0.8

• 0.2

• 0.5

$\int \left(\frac{4{\mathrm{e}}^{\mathrm{x}} - 25}{2{\mathrm{e}}^{\mathrm{x}} - 5}\right)\mathrm{dx} = \mathrm{Ax} + \mathrm{Blog}\left(2{\mathrm{e}}^{\mathrm{x}} - 5\right) + \mathrm{c}$, then

• A = 5 and B = 3

• A = 5 and B = - 3

• A = - 5 and B = 3

• A = - 5 and B = - 3

${\int }_{- \frac{\mathrm{\pi }}{2}}^{\frac{\mathrm{\pi }}{2}}\log \left(\frac{2 - \sin \left(\mathrm{x}\right)}{2 + \sin \left(\mathrm{x}\right)}\right)\mathrm{dx}$ is equal to

• 1

• 3

• 2

• 0

$\int \left(\frac{\left({\mathrm{x}}^2 + 2\right){\mathrm{a}}^{\left(\mathrm{x} + {\tan }^{-1}\left(\mathrm{x}\right)\right)}}{{\mathrm{x}}^2 + 1}\right)\mathrm{dx}$ is equal to

• $\log \left(\mathrm{a}\right) . {\mathrm{a}}^{\mathrm{x} + {\tan }^{-1}\left(\mathrm{x}\right)} + \mathrm{c}$

• $\frac{\left(\mathrm{x} + {\tan }^{-1}\left(\mathrm{x}\right)\right)}{\log \left(\log \left(\mathrm{a}\right)\right)} + \mathrm{c}$

• $\frac{{\mathrm{a}}^{\mathrm{x} + {\tan }^{-1}\left(\mathrm{x}\right)}}{\log \left(\mathrm{a}\right)} + \mathrm{c}$

• $\log \left(\mathrm{a}\right)\left(\mathrm{x} + {\tan }^{-1}\left(\mathrm{x}\right)\right) + \mathrm{c}$

The degree and order of the differential equation ${\left[1 + {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^3\right]}^{\frac{7}{3}} = 7\left(\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}\right)$ respectively are

• 3 and 7

• 3 and 2

• 7 and 3

• 2 and 3