Step 1: Identify the relevant Article.
Article 61 of the Indian Constitution lays down the procedure for impeachment of the President; charges of violation of the Constitution may be preferred by either House of Parliament against the sitting President.
Step 2: State the notice period requirement.
Before initiating impeachment proceedings, a written notice signed by not less than one-fourth of the total members of the House must be given; this notice must be delivered 14 days in advance to give the President time to respond.
Step 3: Confirm by elimination.
Options of 7, 21, and 30 days are all incorrect; the Constitution specifically mandates a 14-day notice period under Article 61, balancing procedural fairness with the gravity of the impeachment process.
\[ \boxed{\text{14 days}} \]