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

Here is Why You Need An Adapter

The outlet and plug type used in Bhutan are C, D and G 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

Bhutan

In Bhutan, outlets of type C, D and G are in use.

Type C

Type D

Type G