Bulk modulus of water is $2 \times 10^9 \ N/m^2$. The pressure required to increase the volume of water by $0.1 \%$ in $N/m^2$ is:

In a meter bridge,a $30 \Omega$ resistance is connected in the left gap and a pair of resistances $P$ and $Q$ in the right gap. Measured from the left,the balance point is $37.5 \text{ cm}$ when $P$ and $Q$ are in series,and $71.4 \text{ cm}$ when they are in parallel. The values of $P$ and $Q$ (in $\Omega$) are:

If $X$ is a Poisson variate such that $\alpha = P(X=1) = P(X=2)$,then $P(X=4)$ is equal to

The logical statement $(\sim(\sim p \vee q) \vee(p \wedge r)) \wedge(\sim q \wedge r)$ is equivalent to

$A$ ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotational motion. Find the speed of the ball at which there will be rolling without slipping.

$A$ gas mixture consists of $2$ moles of $O_2$ and $4$ moles of $Ar$ at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system is: (in $RT$)