Which of the following banks is in charge of India’s banking and monetary system?

The correct option is RBI.

Explanation:
The Reserve Bank of India (RBI) is the central bank of India. Established on April 1, 1935, under the Reserve Bank of India Act, 1934, it acts as the supreme monetary authority entrusted with the responsibility of controlling, issuing, and maintaining the supply of the Indian rupee, as well as regulating the nation's banking system.

Key Functions of the Reserve Bank of India:
1. Monetary Authority: Formulates, implements, and monitors India's monetary policy to control inflation and maintain price stability while fostering economic growth.
2. Regulator and Supervisor: Prescribes broad parameters of banking operations within which the country's banking and financial system functions.
3. Issuer of Currency: Responsible for the issuance, supply, and management of currency notes and coins in India.
4. Banker to the Government: Performs key banking operations for both the Central and State Governments.
5. Banker to Banks: Maintains banking accounts of all scheduled banks and acts as the lender of last resort.

Overview of Other Options:
• SBI (State Bank of India): A public sector commercial bank, not the central regulatory authority.
• BOB (Bank of Baroda): A public sector commercial bank.
• Union Bank: A public sector commercial bank operating under the regulation of the RBI.