Let's analyze the given statements one by one in detail:

Statement (I): The mean free path of gas molecules is inversely proportional to the square of molecular diameter.

The mean free path ($ \lambda $) of gas molecules is the average distance a molecule travels before colliding with another molecule. The formula for the mean free path in terms of molecular diameter ($ d $) is given by:

$$\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}$$

Here, $ k_B $ is the Boltzmann constant, $ T $ is the temperature, and $ P $ is the pressure. From this equation, it is evident that the mean free path ($ \lambda $) is inversely proportional to the square of the molecular diameter ($ d^2 $). Hence, Statement I is true.

Statement (II): Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.

The average kinetic energy ($ E_{\text{avg}} $) of gas molecules is given by:

$$E_{\text{avg}} = \frac{3}{2} k_B T$$

where $ k_B $ is the Boltzmann constant and $ T $ is the absolute temperature. This shows that the average kinetic energy is directly proportional to the absolute temperature of the gas. Hence, Statement II is true.

Considering the analysis above, the correct answer is:

Option B
Both Statement I and Statement II are true