The correct answer is (b), Government.
The Prime Minister of India is the head of the Union Government, which is the executive branch of the Government of India. The Prime Minister is appointed by the President of India, and is responsible to the Parliament of India. The Prime Minister is the chief adviser to 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 Parliament of India. The Prime Minister chooses the other members of the Union Council of Ministers, which is the cabinet of the Government of India. The Prime Minister is also the commander-in-chief of the Indian Armed Forces.
The Prime Minister is a powerful position, and the person who holds the office is one of the most important people in India. The Prime Minister is responsible for making decisions that affect the lives of millions of people, and is the face of the Government of India to the world.
The other options are incorrect. The Prime Minister is not the head of the State, which is the President of India. The Prime Minister is also not the head of both the State and the Government. The Prime Minister is not the head of neither the State nor the Government.