Step 1: Understanding the Constitutional Provision
The question asks to whom the President of India submits their resignation letter. This procedure is specified in the Constitution of India.
Step 2: Recalling Article 56
Article 56(1)(a) of the Constitution of India states that the President holds office for a term of five years from the date on which they enter upon their office. The proviso to this clause states: "the President may, by writing under his hand addressed to the Vice-President, resign his office".
Furthermore, Article 56(2) requires the Vice-President to forthwith communicate the resignation to the Speaker of the Lok Sabha.
Step 3: Evaluating the Options
(A) Chief Justice of India: The Chief Justice administers the oath of office to the President, but the resignation is not submitted to them.
(B) Prime Minister: The President appoints the Prime Minister, but the resignation is not addressed to them.
(C) Vice President: This is the correct authority to whom the President's resignation is addressed, as per Article 56(1)(a).
(D) Speaker of Loksabha: The Vice-President informs the Speaker of the resignation, but the letter is not addressed to the Speaker.
Step 4: Final Answer
The President of India addresses their resignation letter to the Vice President. Therefore, option (C) is the correct answer.