A

Step 1: Understanding the constants
We will analyze the dimensional formulas of each physical constant from Column I to identify its correct representation from Column II.

Step 2: Review the constants:
(i) **Boltzmann constant (k)**: This constant relates the average kinetic energy of particles in a gas with the temperature of the gas. Its dimensional formula is given as, $[M^0 L^0 T^0] mole^{-1}$, which implies it has no dimensions (it is a pure number) when considering one mole of particles.

(ii) **Avogadro constant (N_A)**: This constant gives the number of entities (atoms, molecules) in one mole of a substance. Its dimensional formula is given as, $[M^1 L^2 T^{-2} K^{-1}] mole^{-1}$. This is correct as it relates to energy (which has dimension of mass, length, and time).

(iii) **Gas constant (R)**: It connects the energy scale to the temperature scale in the ideal gas law. The dimensional formula is $[M^1 L^5 T^{-2}]$. This indicates that it involves energy per volume per temperature, which is typical for the gas law.

(iv) **Van der Waals constant (a and b)**: These constants are used in the van der Waals equation for real gases. The a constant relates to the attraction between molecules and has dimensions of $[M^1 L^2 T^{-2} K^{-1}]$. This also includes temperature dependency and relates back to pressure.

Step 3: Match the dimensional formulas:

• **Boltzmann constant** – matches with **[A]**
• **Avogadro constant** – matches with **[B]**
• **Gas constant** – matches with **[C]**
• **Van der Waals constant** – matches with **[D]**

Step 4: Verification:
From the provided constants in Column I and matching all with the dimensional formulas in Column II, we find that only the dimensional formula for the Boltzmann constant corresponds to the entry [A].

Therefore, the correct answer is option A.