According to the Preamble, which term signifies that the head of the Indian…

Concept

The terms in a constitutional preamble describe distinct attributes of the state. To identify a term, match the institutional rule in the question with the term’s precise constitutional meaning.

A republic is a form of state in which the supreme public office is not inherited through a ruling family; the head of state is chosen under the constitutional process.

Application

The question describes an elected, non-hereditary head of the Indian state. That institutional rule is the defining feature of a republic.

Contrast

• Secular concerns the state’s relationship with religions.

• Democratic concerns government based on the authority and participation of the people.

• Socialist concerns the constitutional commitment to social and economic justice.

Cross-check

India’s President is elected for a fixed term rather than inheriting office. This independently confirms the republican character described in the question.

Result

Therefore, the term is Republic.