If a set $A$ has $n$ elements,then the total number of subsets of $A$ is:

$A$ sample of $0.1 \text{ g}$ of water at $100^{\circ} \text{C}$ and normal pressure $(1.013 \times 10^5 \text{ Nm}^{-2})$ requires $54 \text{ cal}$ of heat energy to convert to steam at $100^{\circ} \text{C}$. If the volume of the steam produced is $167.1 \text{ cc}$,the change in internal energy of the sample is ....... $\text{J}$.

Apart from tetrahedral geometry,another possible geometry for $CH_4$ is square planar with the four $H$ atoms at the corners of the square and the $C$ atom at its centre. Explain why $CH_4$ is not square planar?

$A$ bucket filled with water is tied to a rope of length $0.5 ~m$ and is rotated in a circular path in a vertical plane. The minimum velocity it should have at the lowest point of the circle so that the water does not spill is,$(g = 10 ~m/s^2)$.

If $\sin ^{-1}\left(\frac{x}{13}\right)+\operatorname{cosec}^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2}$,then the value of $x$ is

The frequency of a light ray is $6 \times 10^{14} \ Hz$. Its frequency when it propagates in a medium of refractive index $1.5$ will be: