Hin/Bih: दरभंगा darbhanga
‘Gateway to Bengal’ City/District, Bihar
From Darbhangi Khan; or Hin: दर dar, ‘door’, ‘gateway’; and भंग, bhāṅg, ‘breach’, ‘split’ or ‘hemp’ [Cannabis sativa].
None of the derivations seem particularly satisfactory.
Darbhanga is probably more of a gateway to Nepal than Bengal (Raj Darbhanga was a dynasty ruling territories now split between Bihar and Nepal) and the name Darbhangi Khan matches no known ruler, so this is guesswork too.darbhanga
Darbhanga has a long artistic, musical and literary tradition and is known as the ‘Cultural Capital of Bihar’.
It is the oldest city in the Maithili-speaking Mithila region and is called the ‘Heart of Mithilaanchal’.
For related place names see Indian Place names and Bihar place names.

Darbhanga Airport, Darbhanga ElvishRoy99
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