11.

From a group of 8 boys and 3 girls, a commitee of 5 members to be formed. Find the probability that 2 particular girls are included in the committe is

• $\frac{4}{11}$

• $\frac{2}{11}$

• $\frac{6}{11}$

• $\frac{8}{11}$

Equation of the plane passing through (- 2, 2, 2) and (2, - 2, - 2) and perpendicular to the plane 9x - 13y - 3z = 0 is

• 5x + 3y + 2z = 0

• 5x - 3y + 2z = 0

• 5x - 3y - 2z = 0

• 5x + 3y - 2z = 0

The maximum value of z = 9x + 13y subject to 2x + 3y $\le$ 18, 2x + y $\le$ 10, x $\ge$ 0, y $\ge$ 0 is

• 130

• 81

• 79

• 99

$\int \left[\sin \left(\log \left(\mathrm{x}\right)\right) + \cos \left(\log \left(\mathrm{x}\right)\right)\right]\mathrm{dx}$ is equal to

• $\mathrm{xcos}\left(\log \left(\mathrm{x}\right)\right) + \mathrm{c}$

• $\cos \left(\log \left(\mathrm{x}\right)\right) + \mathrm{c}$

• $\mathrm{xsin}\left(\log \left(\mathrm{x}\right)\right) + \mathrm{c}$

• $\sin \left(\log \left(\mathrm{x}\right)\right) +\hspace{0.17em}\mathrm{c}$

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

• $\frac{{\mathrm{e}}^{\mathrm{x}}}{{\mathrm{x}}^2} + \mathrm{c}$

• $\frac{- {\mathrm{e}}^{\mathrm{x}}}{{\mathrm{x}}^2} + \mathrm{c}$

• $\frac{{\mathrm{e}}^{\mathrm{x}}}{\mathrm{x}} + \mathrm{c}$

• $\frac{- {\mathrm{e}}^{\mathrm{x}}}{\mathrm{x}} + \mathrm{c}$

${\int }_5^{10}\frac{1}{\left(\mathrm{x} - 1\right)\left(\mathrm{x} - 2\right)}\mathrm{dx}$

• $\log \left(\frac{27}{32}\right)$

• $\log \left(\frac{32}{27}\right)$

• $\log \left(\frac{8}{9}\right)$

• $\log \left(\frac{3}{4}\right)$

General solution of the differential equation 

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{x} + \mathrm{y} + 1}{\mathrm{x} + \mathrm{y} - 1}$ is given by

• $\mathrm{x} + \mathrm{y} = \log \left|\mathrm{x} + \mathrm{y}\right| + \mathrm{c}$

• $\mathrm{x} - \mathrm{y} = \log \left|\mathrm{x} + \mathrm{y}\right| + \mathrm{c}$

• $\mathrm{y} = x + \log \left|\mathrm{x} + \mathrm{y}\right| + \mathrm{c}$

• $\mathrm{y} = \mathrm{xlog}\left|\mathrm{x} + \mathrm{y}\right| + \mathrm{c}$

The order and degree of the differential equation $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} = \sqrt[3]{1 - {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^4}$ are respectively

• 2, 3

• 3, 2

• 2, 4

• 2, 2

Form the differential equation of all family of lines y = mx ± $\frac{4}{\mathrm{m}}$ eliminating the arbitrary m constant 'm' is

• $\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2} = 0$

• $\mathrm{x}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) - \mathrm{y}\frac{\mathrm{dy}}{\mathrm{dx}} +\hspace{0.17em}4 = 0$

• $\mathrm{x}{\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2 + \mathrm{y}\frac{\mathrm{dy}}{\mathrm{dx}} +\hspace{0.17em}4 = 0$

• $\frac{\mathrm{dy}}{\mathrm{dx}} = 0$

If 'f' is the angle between the lines ax² + 2hxy + by² = 0, then angle between x² + 2xy sec$\left(\mathrm{\theta }\right)$ + y² = 0 is

• $\mathrm{\theta }$

• $2\mathrm{\theta }$

• $\frac{\mathrm{\theta }}{2}$

• $3\mathrm{\theta }$