Introduction:
In the given analogy, the relationship between India and its President is being compared to the relationship between a State and an entity. We need to determine the correct entity that completes the analogy.

Analogy:
India : President :: State : ?

Explanation:
To understand the analogy better, let's break it down into its components:

India:
India is a country located in South Asia. It is the seventh-largest country by land area and the second-most populous country in the world. India is a democratic country and follows a parliamentary system of government.

President:
The President of India is the head of state and the first citizen of the country. The President is elected by an electoral college consisting of the elected members of both houses of Parliament and the Legislative Assemblies of the States. The President's role is mainly ceremonial and symbolic, with limited executive powers.

State:
In the context of India, a state refers to the administrative divisions of the country. India is divided into 28 states and 8 union territories. Each state has its own government and is headed by a Chief Minister.

Chief Minister:
The Chief Minister is the elected head of the government of a state. The Chief Minister is appointed by the Governor of the state, who is a representative of the President at the state level. The Chief Minister is responsible for the administration and governance of the state.

Conclusion:
Based on the given analogy, the correct entity that completes the analogy is Chief Minister. Just as the President is the head of India, the Chief Minister is the head of a state in India. Therefore, option C) Governor is the correct answer.