The head of the executive branch of the Tamil Nadu government is the:

President
Prime Minister
Governor
Chief Minister

The correct answer is: d) Chief Minister.

The Chief Minister is the head of the executive branch of the Tamil Nadu government. The Chief Minister is the leader of the party or coalition that has the most seats in the Tamil Nadu Legislative Assembly. The Chief Minister is appointed by the Governor of Tamil Nadu, who is the head of state of Tamil Nadu. The Chief Minister is responsible for the day-to-day running of the government and for appointing the ministers in the state cabinet.

The President is the head of state of India. The President is elected by an electoral college consisting of members of both houses of the Indian Parliament and the legislative assemblies of the states. The President is the supreme commander of the Indian Armed Forces and has the power to veto legislation passed by Parliament.

The Prime Minister is the head of government of India. The Prime Minister is appointed by the President and is responsible for the day-to-day running of the government. The Prime Minister is the leader of the party or coalition that has the most seats in the Lok Sabha, the lower house of the Indian Parliament.

The Governor is the head of state of a state in India. The Governor is appointed by the President of India. The Governor is the supreme commander of the state police force and has the power to dissolve the state legislature and call for fresh elections.