The correct answer is option 2, The Chief Justice of India. During the inauguration ceremony for the new President, the Chief Justice of India administers the oath of office. This is in accordance with Article 60 of the Indian Constitution, which states that the President shall make and subscribe to an oath or affirmation before entering office. The Chief Justice of India, being the head of the judiciary, is responsible for conducting the swearing-in ceremony. It is important to note that the Chief Election Commissioner, option 1, is not involved in this process. The outgoing President, option 3, does not administer the oath, but rather hands over the responsibilities of the office to the new President. The Vice President, option 4, also does not administer the oath, as their role is to preside over the Rajya Sabha, the Upper House of Parliament.