Easy in theory but different in reality. Most of the banks will outright refuse to accept foreign currency for deposit. I had some extra foreign currency after I returned from tour but all banks I went to (both PSU and pvt banks), refused to deal with it. That includes icici, hdfc, idfc, sbi, union bank. Every bank I went to said "this is not possible". And there are not some rural branches, rather all are in big metro city branches.
Forget foreign currency cash deposit, I went to to SBI for foreign remittance to sister. As soon as I said, "I want to send money to Sweden" the immediate reply was "no, no, no, no, no. Sending money to foreign country is not allowed".
How funny. I returned home and sent from SBI netbanking. I knew it could be done online, but I went to branch to ask about the fees for transfer. But the way he said 5 times "no", and "not allowed" it felt like I said something criminal. (yes I counted those 5 times "no").