If $u = x y^2 \tan^{-1}\left(\frac{y}{x}\right)$, then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$ is equal to

Which tissue provides mechanical support to the young stem and petiole of leaves?

$A$ ping-pong ball of mass $m$ is floating in air by a jet of water emerging out of a nozzle. If the water strikes the ping-pong ball with a speed $v$ and just after collision the water falls dead,the mass flow rate of water in the nozzle is equal to

The dispersive powers of the materials of two lenses forming an achromatic combination are in the ratio of $4: 3$. If the effective focal length of the two lenses is $+60 ~cm$,then the focal lengths of the lenses should be:

The bob of a simple pendulum is displaced from its equilibrium position $O$ to a position $Q$ which is at height $h$ above $O$ and the bob is then released. Assuming the mass of the bob to be $m$ and time period of oscillations to be $2.0\ s$,the tension in the string when the bob passes through $O$ is

Which of the following has the smallest size?