The lengths of the shadows of a tree of height p, thrown by sun's rays at three different moments are p, 2p and 3p. The sum of the angles of elevation of the sun's rays at these three moments is equal to...

A cuboid has volume $V = l \times l \times \sqrt{l}$, where $l$ is the length of one side. When the length $l$ is measured by a meter scale of least count $1\,\text{mm}$, the relative percentage error in the measurement of its volume is $6.25\%$. Then the relative percentage error in measurement of its length and the value of the length $l$ is

A particle is performing U.C.M. along a circle of radius $R$. In half the period of revolution, its displacement and distance covered are respectively

The equation of the trajectory of a ball projected at an angle $\theta$ with the horizontal, is given as $y = x - \dfrac{gx^2}{2}$
The initial velocity of the ball is
[Given : $\tan 45^\circ = 1$, $\cos 45^\circ = \dfrac{1}{\sqrt{2}}$ ]