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

Here is Why You Need An Adapter

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

Bangladesh

In Bangladesh, outlets of type A, C, D, G and K are in use.

Type A

Type C

Type D

Type G

Type K