You Do Need power plug adapter while traveling from India to Faroe Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Faroe Islands are C, E, F and K and in India are C, D and M. This is how they look like.

India

In India, outlets of type C, D and M are in use.

Type C

Type D

Type M

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K