Step 1: Recall RBI's start.
The Reserve Bank of India was set up under the RBI Act, 1934 and began work on 1 April 1935. At first it was a privately owned shareholders' bank.
Step 2: Need for nationalisation.
After independence the government wanted public control over money and banking. So it decided to take over the RBI.
Step 3: The process.
Through the Reserve Bank (Transfer to Public Ownership) Act, 1948, private shareholders were paid off and ownership moved to the government.
Step 4: The date.
This nationalisation came into effect on 1 January 1949.
Step 5: Conclude.
So the RBI was nationalised in 1949.
Answer: 1949