Step 1: Understanding the Question:
The prompt seeks the specific institution tasked with setting and managing the repo rate within India.
Step 2: Detailed Explanation:
The Repo Rate is the specific interest rate at which a nation's central bank provides short-term loans to commercial banks facing fund deficits.
For India, this central banking authority is the Reserve Bank of India (RBI).
The RBI's Monetary Policy Committee (MPC) convenes periodically to adjust the repo rate, aiming to manage inflation and foster economic expansion.
Step 3: Final Answer:
The correct choice is (C).