The correct answer is: D. all of the above
Inverse definite mean time (IDMT) relays are used for overcurrent and earth fault protection of transformers against heavy loads, internal short-circuits, and external short-circuits.
IDMT relays are a type of overcurrent relay that is designed to provide a time delay for overcurrents that are caused by heavy loads. This time delay allows the transformer to continue to operate normally even when there is a temporary increase in load. However, if the overcurrent is caused by an internal short-circuit, the IDMT relay will trip the transformer off quickly to prevent damage.
IDMT relays are also used for earth fault protection of transformers. Earth faults can occur when there is a current that flows from the transformer windings to the ground. This can happen if there is a fault in the insulation of the transformer windings or if there is a foreign object that comes into contact with the transformer. When an earth fault occurs, the IDMT relay will trip the transformer off quickly to prevent damage.
IDMT relays are a valuable tool for protecting transformers from overcurrent and earth fault conditions. They provide a time delay for overcurrents that are caused by heavy loads, and they trip the transformer off quickly for internal short-circuits and earth faults.