@powerful-state-7137 I have accounts with both Kotak & ICICI and have been able to negotiate better rates with ICICI.
I think they have something like 17 - 20p / USD and Kotak was around 40p
Depends on a lot of factors (how much is incoming, your relationship with them, etc) but considering ICICI does a lot of Inward remittances, they seem to provide better rates.