If a person A is moving with velocity 2 km/h, person B is moving with velocity 3 km/h and the angle between the direction of movements of A and B is 60°, then the velocity of A relative to B in the direction of A is

• $\sqrt{13 - 6\sqrt{3}}$

• $\sqrt{13 + 6\sqrt{3}}$

• $\sqrt{7}$

• $\sqrt{19}$

The intersection angle of the curve xy = a² and x² - y² = a² is

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{5\mathrm{\pi }}{6}$

The point of intersection of line $\frac{\mathrm{x} - 6}{- 1} = \frac{\mathrm{y} + 1}{0} = \frac{\mathrm{z} + 3}{4}$ and plane x + y - z = 3 is

• (2, 1, 0)

• (7, - 1, - 7)

• (1, 2, - 6)

• (5, - 1, 1)

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

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

• rectangle

• rhombus

• trapezium

• parallelogram

If the resultant of two forces of magnitude P and P$\sqrt{3}$ acting on a particle is of magnitude P, then the angle between them is

• 60°

• 120°

• 90°

• 150°

277.

A particle is dropped from a height 12 g metre and 4 s after anotherparticle is projected from the ground towards it with a velocity 4g ms. The time after which the second particle meets first is

• 4 s

• 2 s

• $\frac{1}{2} \mathrm{s}$

• 1 s

A uniform ladder rests in limiting equilibrium with its lower end on a rough horizontal plane with coefficient of friction µ and its upper end against a smooth vertical wall. If $\mathrm{\theta }$ is the inclination of the ladder with the wall, then $\mathrm{\theta }$ is equal to

• ${\tan }^{-1}\left(\mathrm{u}\right)$

• ${\cot }^{-1}\left(\mathrm{u}\right)$

• ${\cot }^{-1}\left(2\mathrm{u}\right)$

• ${\tan }^{-1}\left(2\mathrm{u}\right)$

A plane which passes through the point (3, 2, 0) and the line $\frac{\mathrm{x} - 3}{1} = \frac{\mathrm{y} - 6}{5} = \frac{3 - 4}{4}$ is

• x - y + z = 1

• x + y + z = 5

• x + 2y - z = 0

• 2x - y + z = 5

If the planes x + 2y + kz = 0 and 2x + y - 2z = 0, are at right angles, then the value of k is

• 2

• - 2

• $\frac{1}{2}$

• $- \frac{1}{2}$