$A$ body of mass $6 ~kg$ is under a force which causes displacement in it given by $s = \frac{t^2}{4}$ metres,where $t$ is time. The work done by the force in $2$ seconds is: (in $~J$)

The temperature of $5$ moles of a gas at constant volume is changed from $100^{\circ} C$ to $120^{\circ} C$. The change in internal energy is $80 \ J$. The total heat capacity of the gas at constant volume in $J/K$ is:

If $\log _{27}(\log _3 x) = \frac{1}{3}$, then the value of $x$ is

An engine giving a whistle is moving towards a stationary observer with a speed of $110\,m/s$. What will be the ratio of the frequency of the whistle heard when the engine is approaching and receding from the observer? (The speed of sound is $330\,m/s$.)

In a transformer,the number of turns in primary and secondary are $500$ and $2000$ respectively. If current in primary is $48 \ A$,the current in the secondary is........$A$

$A$ particle of mass $m$ moves with a velocity $v$ along the line $PC$ (as shown in the figure). The angular momentum of the particle about point $O$ is: