Answer:
This is a bit of a trick question. The short answer is yes, and yes. Darjeeling is in both West Bengal and North Bengal.
Darjeeling is a district of India, located in the West Bengal state.
North Bengal is not an official state, but rather, a casual or informal term used to refer to a region which includes the northern part of West Bengal in India, as well as the northern part of Bangladesh. And "North Bengal" definitely includes Darjeeling.