Step 1: Separate the drafting stage from the approval stage.
India's Five Year Plans were first prepared in draft form by the Planning Commission, which set targets and allocated funds across sectors.
Step 2: Identify who gives the final go-ahead.
The draft plan was then placed before the National Development Council, a body made up of the Prime Minister, Union Cabinet ministers, and the Chief Ministers of all states, and this council gave the plan its final approval.
Step 3: Rule out the other bodies.
The Union Cabinet handles day-to-day government decisions but not this specific approval step. The President's role in this process is only formal, and the Planning Commission's job ends at drafting, not approving.
Final Answer:
The National Development Council approves the Five Year Plans, so option C is correct. \[ \boxed{\text{National Development Council}} \]