$\lim _{x \rightarrow 0} \frac{\sin x \sin ^{-1} x}{x^2}$ is equal to

In a reaction,$A + B \rightleftharpoons C + D$,$40 \%$ of $B$ has reacted at equilibrium,when $1 \ mole$ of $A$ was heated with $1 \ mole$ of $B$ in a $10 \ L$ closed vessel. The value of $K_C$ is

Fraunhofer lines are produced by the absorption of light in

$A$ uniform rod of mass $m$ and length $l$ is moving with velocity $u$ in a direction perpendicular to its length. $A$ blow of impulse $J$ is given perpendicular to its length at a distance $\frac{l}{4}$ from its centre at point $P$ such that the instantaneous velocity of point $P$ becomes $2u$. Then the velocity of its centre of mass will be:

In $\triangle ABC$,if $\frac{1}{b+c} + \frac{1}{c+a} = \frac{3}{a+b+c}$,then $C$ is equal to (in $^{\circ}$)

........ of a reaction cannot be determined experimentally.