$A$ body of mass $m$ and radius of gyration $K$ has an angular momentum $L$. Then its angular velocity is

$A$ body falling from a height of $10\,m$ rebounds from a hard floor. If it loses $20\%$ of its energy on impact,then the coefficient of restitution is:

If $f:[2, \infty) \rightarrow B$ defined by $f(x)=x^2-4x+5$ is a bijection,then $B$ is equal to

For the reactions:
$2NO + O_2 \rightleftharpoons 2NO_2 ; K_1$
$4NO + 2Cl_2 \rightleftharpoons 4NOCl ; K_2$
$NO_2 + 1/2 Cl_2 \rightleftharpoons NOCl + 1/2 O_2 ; K_3$
where $K_1, K_2, K_3$ are equilibrium constants,then $K_3^2$ is equal to:

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

$y=e^{a \sin ^{-1} x} \Rightarrow (1-x^2) y_{n+2}-(2 n+1) x y_{n+1}$ is equal to