Banker to the governments: the Reserve Bank serves every State except Sikkim, and compiles the accounts at Nagpur

The Reserve Bank of India Act, 1934 requires the Central Government to entrust the Reserve Bank with all its money, remittance, exchange and banking transactions in India and with the management of its public debt.
The Reserve Bank may by agreement also act as banker and debt manager to State Governments, and it acts as banker to all the State Governments in India except Sikkim, for which it has a limited agreement covering the management of public debt.
Ways and Means Advances are short-term interest bearing advances given to governments to meet temporary mismatches in their receipts and payments, and the rate of interest on them is linked to the repo rate.
For State Governments the scheme has a Special Drawing Facility against the collateral of government securities held by the State, and a normal Ways and Means Advance once that limit is exhausted.
A withdrawal beyond the Ways and Means Advances limit is treated as an overdraft.
Surplus balances of State Governments are invested automatically in Government of India 14-day Intermediate Treasury Bills.
Banking business for the governments is carried out by the Public Accounts Departments at Reserve Bank offices, while public debt is managed by the Internal Debt Management Department and the Public Debt Offices.
Final compilation of the Government accounts of the Centre and the States is done at the Nagpur office of the Reserve Bank, which has a Central Accounts Section.

State for which the Reserve Bank is not banker: Sikkim Instrument for investing State surplus balances: Government of India 14-day Intermediate Treasury Bills Office that compiles Central and State government accounts: Nagpur
Why it matters for exams: The Sikkim exception, the Ways and Means Advances mechanism and the Nagpur Central Accounts Section are classic one-mark questions on the Reserve Bank's role as banker to governments.
Kerala PSCUPSCBank

In plain words

WMA Ways and Means Advances — A short-term interest bearing advance from the Reserve Bank to a government to bridge a temporary mismatch between receipts and payments.

SDF Special Drawing Facility — In the State Government scheme, the first slab of accommodation, given against the collateral of government securities held by the State.