In an ideal gas at temperature $T$,the average force that a molecule applies on the walls of a closed container depends on $T$ as $T^q$. $A$ good estimate for $q$ is:

An $X$-ray tube produces a continuous spectrum of radiation with its shortest wavelength of $45 \times 10^{-2} \text{ \AA}$. The maximum energy of a photon in the radiation in $eV$ is $(h = 6.62 \times 10^{-34} \text{ J-s}, c = 3 \times 10^8 \text{ m/s})$. (in $27,500$)

Which one of the following represents the graph between $\log p$ (on $Y$-axis) and $\frac{1}{T}$ (on $X$-axis)?
($p=$ vapour pressure of a liquid,$T=$ absolute temperature)

If $A$ is an invertible matrix of order $n$,then the determinant of $\operatorname{adj} A$ is equal to :

The refractive index of a material of a plano-concave lens is $5/3$,and the radius of curvature is $0.3 ~m$. The focal length of the lens in air is (in $~m$)

In the given figure,what does the part labeled '$a$' represent?