The head of state of India is the President. However, in terms of executive powers, the Prime Minister wields more influence and is considered the head of government. Here is a point-wise breakdown:

• The President of India is the ceremonial head of state and represents the country both domestically and internationally.
• The President is elected by an electoral college comprising members of both houses of Parliament and state legislatures.
• The President's role is largely constitutional and symbolic, with limited executive powers.
• The President appoints the Prime Minister, who is the head of government.
• The Prime Minister, along with the Council of Ministers, holds the real executive power and is responsible for the day-to-day governance of the country.
• The President, upon the advice of the Prime Minister, appoints and dismisses ministers, diplomats, judges, and other government officials. However, these decisions are usually formalities carried out as per the advice of the Prime Minister and the Council of Ministers.

In conclusion, while the President of India is the head of the nation, the Prime Minister exercises greater control as the head of government.