**Explanation:**

The principle of entropy is a fundamental concept in thermodynamics that relates to the dispersal of energy and the tendency of a system to move towards a state of greater disorder. It is often described as a measure of the "randomness" or "disorder" of a system.

**a) Transfer of heat through a finite temperature difference:**

When heat is transferred between two objects that are at different temperatures, it flows from the hotter object to the colder object until they reach thermal equilibrium. This process can be described in terms of entropy because the heat transfer tends to increase the overall randomness or disorder of the system. As heat flows, the energy becomes more evenly distributed, increasing the entropy of the system.

**b) Mixing of two fluids:**

When two fluids are mixed, their particles become more randomly arranged, leading to an increase in disorder or randomness. This mixing process is accompanied by an increase in entropy because the energy becomes more dispersed and distributed among the particles. Therefore, the mixing of two fluids can be regarded as applying the principle of entropy.

**c) Maximum temperature attainable from two finite bodies:**

The maximum temperature that can be attained by two finite bodies is determined by the second law of thermodynamics, which is closely related to the principle of entropy. According to the second law, heat flows spontaneously from a hotter object to a colder object, and it is not possible to transfer heat from a colder object to a hotter object without the input of external energy. This limitation is due to the increase in entropy that occurs when heat flows from a hotter body to a colder body. Therefore, the concept of maximum temperature attainable from two finite bodies is based on the principle of entropy.

**d) All of the mentioned:**

All of the mentioned situations - transfer of heat through a finite temperature difference, mixing of two fluids, and the maximum temperature attainable from two finite bodies - involve processes that are related to the principle of entropy. In each case, there is an increase in disorder or randomness, leading to an increase in the entropy of the system. Therefore, option 'D' is correct as all of the mentioned situations can be regarded as applying the principle of entropy.