Explanation:

The Reserve Bank of India (RBI) was established on April 1, 1935, in accordance with the Reserve Bank of India Act, 1934. It was initially set up as a private share-holders' bank but was nationalized in 1949. Its central office was initially established in Calcutta but was permanently moved to Mumbai in 1937. Option (2) is the correct year of establishment. Options (1), (3), and (4) are incorrect dates. $1932$ predates the RBI Act. $1940$ is after its establishment. $1947$ is the year of India's independence, after which the RBI continued to function as the central bank.