When zeolite,which is a hydrated sodium aluminium silicate,is treated with hard water,the sodium ions are exchanged with which of the following?

Two rings of radius $R$ and $nR$ made of the same material have a ratio of moment of inertia about an axis passing through their centers and perpendicular to their planes as $1:8$. The value of $n$ is (mass per unit length is constant).

One mole of calcium phosphide on reaction with excess of water gives

$A$ ball of mass $M$ falls from a height $h$ on a floor for which the coefficient of restitution is $e$. The height attained by the ball after two rebounds is

$A$ particle is projected vertically upwards from a point $A$ on the ground. It takes time $t_1$ to reach a point $B$,and it continues to move up. If it takes a further time $t_2$ to reach the ground from point $B$,then the height of point $B$ from the ground is:

The coordinates of the point $P$ on the curve $x=a(\theta+\sin \theta), y=a(1-\cos \theta)$,where the tangent is inclined at an angle $\frac{\pi}{4}$ to the $x$-axis,are