$A$ thief is running away on a straight road in a jeep moving with a speed of $9 \, m/s$. $A$ policeman chases him on a motorcycle moving at a speed of $10 \, m/s$. If the instantaneous separation between the jeep and the motorcycle is $100 \, m$,how long will it take for the police to catch the thief? (in $s$)

If $\tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\frac{\pi}{2}$,then $1-xy-yz-zx$ is equal to

Which of the following is not a polymer?

$A$ particle of mass $4 M$ which is initially at rest explodes into three pieces of masses $M$,$M$ and $2 M$. The equal masses move along $X$ and $Y$-axes with velocities $4 ~ms^{-1}$ and $6 ~ms^{-1}$,respectively. The magnitude of the velocity of the heavier mass is

$A$ point object is placed at a distance of $30 \, cm$ from a convex mirror of focal length $30 \, cm$. The image will form at

The rate of steady volume flow of water through a capillary tube of length $l$ and radius $r$ under a pressure difference of $P$ is $V$. This tube is connected with another tube of the same length but half the radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is $P$).