The correct answer is (b) Chief Minister.
The Chief Minister is the head of the state government in Sikkim. The Chief Minister is appointed by the Governor of Sikkim, who is the head of state. The Chief Minister is responsible for the day-to-day running of the state government and for appointing the members of 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 Parliament and the legislative assemblies of the states. The President is responsible for appointing the Prime Minister and the other members of the Union Council of Ministers.
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 central government. The Prime Minister is also the leader of the party or coalition that has the most seats in the Lok Sabha, the lower house of Parliament.
The Governor is the head of state of Sikkim. The Governor is appointed by the President of India. The Governor is responsible for appointing the Chief Minister and the other members of the state cabinet. The Governor also has the power to dissolve the state assembly and to call for fresh elections.