If ${\left(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}\right)}^2 + {\left(\overrightarrow{\mathrm{a}} . \overrightarrow{\mathrm{b}}\right)}^2 = 676 \mathrm{and} \left|\overrightarrow{\mathrm{b}}\right|$ = 2, then $\left|\overrightarrow{\mathrm{a}}\right|$ is equal to

• 13

• 26

• 39

• None of these

A particle is thrown with the velocity v with the angle a from the horizontal plane and its range on the horizontal plane is twice to themaximum height gained. Then, $\tan \left(\mathrm{\alpha }\right)$ is equal to

• 9

• 5

• 2

• 1

Two dice are thrown together. Then the probability that the sum of numbers appearing on them is a prime number, is

• $\frac{5}{12}$

• $\frac{7}{18}$

• $\frac{13}{36}$

• $\frac{11}{36}$

The points 0, 2 + 3i, i - 2 - 2i in the argand plane are the vertices of a

• rectangle

• rhombus

• trapezium

• parallelogram

If b > a, then ${\int }_{\mathrm{a}}^{\mathrm{b}}\frac{\mathrm{dx}}{\sqrt{\left(\mathrm{x} - \mathrm{a}\right)\left(\mathrm{b} - \mathrm{x}\right)}}$ is equal to

• $\frac{\mathrm{\pi }}{2}$

• $\mathrm{\pi }$

• $\frac{\mathrm{\pi }}{2}\left(\mathrm{b} - \mathrm{a}\right)$

• $\frac{\mathrm{\pi }}{4}\left(\mathrm{b} - \mathrm{a}\right)$

The solution of differential equation (1 + x)ydx + (1 - y)x dy = 0 is

• ${\log }_{\mathrm{e}}\left(\mathrm{xy}\right) + \mathrm{x} - \mathrm{y} = \mathrm{c}$

• ${\log }_{\mathrm{e}}\left(\frac{\mathrm{x}}{\mathrm{y}}\right) + \mathrm{x} + \mathrm{y} = \mathrm{c}$

• ${\log }_{\mathrm{e}}\left(\frac{\mathrm{x}}{\mathrm{y}}\right) - \mathrm{x} + \mathrm{y} = \mathrm{c}$

• ${\log }_{\mathrm{e}}\left(\mathrm{xy}\right) - \mathrm{x} + \mathrm{y} = \mathrm{c}$

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

• $\frac{- {\mathrm{e}}^{\mathrm{x}}}{\mathrm{x} +\hspace{0.17em}1} + \mathrm{c}$

• $\frac{{\mathrm{e}}^{\mathrm{x}}}{\mathrm{x} +\hspace{0.17em}1} + \mathrm{c}$

• $\frac{{\mathrm{e}}^{\mathrm{x}}\left(\mathrm{x} - 1\right)}{\mathrm{x} +\hspace{0.17em}1} + \mathrm{c}$

• $\frac{{\mathrm{xe}}^{\mathrm{x}}}{\mathrm{x} +\hspace{0.17em}1} + \mathrm{c}$

If $\overrightarrow{\mathrm{a}}$ is any vector, then $\hat{\mathrm{i}} \times \left(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{i}}\right) + \hat{\mathrm{i}} \times \left(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{j}}\right) +\hspace{0.17em}\hat{\mathrm{k}} \times \left(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{k}}\right)$ is equal to

• $\overrightarrow{\mathrm{a}}$

• $2\overrightarrow{\mathrm{a}}$

• $3\overrightarrow{\mathrm{a}}$

• $\overrightarrow{0}$

The product of two times of flight from a point P to another point Q with a given velocity of projection is

• $\frac{\mathrm{PQ}}{\mathrm{g}}$

• $\frac{2\mathrm{PQ}}{\mathrm{g}}$

• $\frac{\mathrm{PQ}}{2\mathrm{g}}$

• $\frac{3\mathrm{PQ}}{\mathrm{g}}$

40.

A stone of mass m is thrown vertically upwards with a velocity of 9.8 ms^-1. The height of the point where KE = PE is (g = 9.8 ms^-2)

• 9.8 m

• 4.9 m

• 2.45 m

• 2 m