Two identical balls $A$ and $B$ are released from the positions shown in figure. They collide elastically on the horizontal portion $MN$. The ratio of the maximum height attained by $A$ and $B$ after the collision will be: (neglect friction)

Equilibrium constant for the reaction $H_2O_{(g)} + CO_{(g)} \rightleftharpoons H_{2(g)} + CO_{2(g)}$ is $81$. If the velocity constant of the forward reaction is $162 \ L \ mol^{-1} \ s^{-1}$,what is the velocity constant (in $L \ mol^{-1} \ s^{-1}$) for the backward reaction?

Evaluate the determinant: $\left|\begin{array}{cc}2 & 4 \\ -5 & -1\end{array}\right|$

If $f(x) = \sin x + \cos x$,then $f\left(\frac{\pi}{4}\right) f^{(iv)}\left(\frac{\pi}{4}\right)$ is equal to

$100 \ g$ of water is heated from $30^{\circ}C$ to $50^{\circ}C$. Neglecting the slight expansion of water,the change in its internal energy is ....... $kJ$? (Specific heat of water = $4184 \ J/kg\cdot K$)

On heating a liquid of coefficient of cubical expansion $\gamma$ in a container having coefficient of linear expansion $\gamma / 3$,the level of liquid in the container will