To open a bank account, you need to provide proof of identity such as a passport, driver's license, PAN card, voter ID, Aadhaar card, or NREGA card, which can also serve as proof of address if it contains your address. If your address proof shows a different address than your current address in Mumbai, you can still open an account by declaring your Mumbai address. Banks require proof of identity and address for Know Your Customer compliance to properly identify customers. If you do not have valid documents, you can open a small account by submitting your photo and signature, but it will have restrictions like lower balance and transaction limits. Alternatively, you may be able to open a full-function account if