Step 1: Constitutional position.
Article 52 provides for a President of India—the {Head of the State/Republic}. The President is the constitutional, ceremonial head of the Union.
Step 2: Distinguish from head of government.
The Prime Minister (Art. 74) is the real executive head of government, not the head of state.
Step 3: Conclude.
\[
\boxed{\text{President (Option A) is the head of the Republic of India.}}
\]