Let's analyze each statement step by step:

For (A): “Pressure varies inversely with volume of an ideal gas.”

At constant temperature (isothermal process), Boyle's law applies:

$$PV = \text{constant}.$$

Thus, pressure and volume have an inverse relationship.

Hence, (A) corresponds to the Isothermal process, which is (III).

For (B): “Heat absorbed goes partly to increase internal energy and partly to do work.”

In a constant pressure (isobaric) process, when heat is supplied, part of it is used to do work (expansion, for example) and the rest increases the internal energy.

Therefore, (B) matches with the Isobaric process, which is (IV).

For (C): “Heat is neither absorbed nor released by a system.”

This implies that the process is adiabatic (no heat exchange).

Thus, (C) matches with the Adiabatic process, which is (I).

For (D): “No work is done on or by a gas.”

Work done by a gas is given by $$W = P\Delta V.$$

If the volume does not change (constant volume), then no work is done.

So, (D) identifies with the Isochoric process, which is (II).

Putting it all together:

(A) → (III) Isothermal process

(B) → (IV) Isobaric process

(C) → (I) Adiabatic process

(D) → (II) Isochoric process

Thus, the correct answer is:

Option D

A-III, B-IV, C-I, D-II.