The area (in square units) of the region bounded by the curves $x=y^2$ and $x=3-2y^2$ is

$A$ uniform rod $AB$ of length $L$ and mass $M$ is lying on a smooth table. $A$ small particle of mass $m$ strikes the rod with a velocity $v_0$ at point $C$ at a distance $x$ from the centre $O$. The particle comes to rest after the collision. The value of $x$,so that point $A$ of the rod remains stationary just after the collision,is:

If $OA$ is equally inclined to $OX, OY$ and $OZ$ and if $A$ is $\sqrt{3}$ units from the origin,then $A$ is:

Removal of shoot tips is a very useful technique to boost the production of tea-leaves. This is because

If the mean and variance of a binomial variate $X$ are $8$ and $4$ respectively,then $P(X < 3)$ equals to

There are two identical small holes of cross-sectional area $a$ on the opposite sides of a tank containing a liquid of density $\rho$. The difference in height between the holes is $h$. The tank is resting on a smooth horizontal surface. The horizontal force which will have to be applied on the tank to keep it in equilibrium is