$6.023 \times 10^{22}$ molecules are present in $10 \ g$ of a substance $x$. The molarity of a solution containing $5 \ g$ of substance $x$ in $2 \ L$ of solution is $\dots \dots \dots \times 10^{-3} \ M$.

Three rings each of mass $M$ and radius $R$ are arranged as shown in the figure. The moment of inertia of the system about $YY'$ will be

The shadow of a tower standing on a level ground is found to be $60 \ m$ longer when the Sun's altitude is $30^{\circ}$ than when it is $45^{\circ}$. The height of the tower is

The function $\sin^2(\omega t)$ represents

The pressure versus temperature graph of an ideal gas is as shown in the figure. The density of the gas at point $A$ is ${\rho _0}$. The density at point $B$ will be

The minimum force required to move a body up an inclined plane is three times the minimum force required to prevent it from sliding down the plane. If the coefficient of friction between the body and the inclined plane is $\frac{1}{2 \sqrt{3}}$,then the angle of the inclined plane is (in $^{\circ}$)