$A$ machine gun fires a bullet of mass $40\, g$ with a velocity $1200\, m/s$. The man holding it can exert a maximum force of $144\, N$ on the gun. How many bullets can he fire per second at the most?

$A$ steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \ mm$ at a certain temperature. The maximum temperature variation allowable during the ruling is .......... $^oC$ (Coefficient of linear expansion of steel $\alpha = 10 \times 10^{-6} \ K^{-1}$)

If $\frac{\tan 3A}{\tan A} = a$,then $\frac{\sin 3A}{\sin A}$ is equal to

One end each of a resistance $r$,a capacitor $C$,and a resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries $P, Q,$ and $R$ having emf's $E, E,$ and $2E$. The negative terminals of the batteries are then connected together. In this circuit,with steady current,the potential drop across the capacitor is:

$A$ rigid body is rotating with variable angular velocity $\omega = (a - bt)$ at any instant of time $t$. The total angle subtended by it before coming to rest will be ($a$ and $b$ are constants).

Let $PQ$ and $RS$ be tangents at the extremities of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle,then $2r$ equals