Which one of following offices is held during the pleasure of the president of India?

Correct Answer: Governor of a state

Explanation:
Under the Constitution of India, certain constitutional offices are held during the "pleasure of the President." This means that the holder of the office can be removed by the President at any time without requiring a specific procedure or parliamentary impeachment.

According to Article 156(1) of the Constitution of India, the Governor of a State holds office during the pleasure of the President. Although the normal term of office for a Governor is five years, the President can remove a Governor from office at any time before the completion of their term.

Let's examine why the other options are incorrect:
1. Vice-President: The Vice-President is elected by an electoral college consisting of members of both Houses of Parliament and is removed by a resolution of the Council of States (Rajya Sabha) passed by an effective majority and agreed to by the House of the People (Lok Sabha).
2. Chief Justice of India: Under Article 124(4), the Chief Justice of India (and other Supreme Court judges) can only be removed by an order of the President passed after an address by each House of Parliament supported by a special majority on the grounds of proved misbehaviour or incapacity.
3. Comptroller and Auditor General of India (CAG): Under Article 148(1), the CAG is removed from office in the like manner and on the like grounds as a Judge of the Supreme Court of India.

Therefore, among the given choices, only the Governor of a state holds office during the pleasure of the President of India.