The correct option is 1 and 3 only.
Explanation
The appointment of the Prime Minister is governed by Article 75 of the Indian Constitution. While the Constitution establishes the authority for appointment, the specific criteria for selecting the appointee rely heavily on established parliamentary conventions rather than explicit constitutional text.
Statement-wise Analysis:
- Statement 1 is Correct: Article 75(1) of the Constitution explicitly mandates that the Prime Minister shall be appointed by the President. This is a formal executive function of the President.
- Statement 2 is Incorrect: The Constitution does not contain any specific provision stating that the leader of the majority party in the Lok Sabha must be appointed as Prime Minister. Article 75 is silent on the procedure of selection. The practice of appointing the leader of the majority party is a fundamental convention of the parliamentary system, not a written constitutional rule.
- Statement 3 is Correct: In the absence of a clear majority (e.g., a coalition government or hung parliament), the President exercises situational discretion. In such cases, the President appoints a leader who, in their judgment, is acceptable to the coalition partners and can prove a majority on the floor of the House.
Key Takeaway:
The Constitution (Article 75) only provides that the President appoints the Prime Minister; it does not codify the procedure for selection. The rule regarding the "leader of the majority party" is a convention, whereas the appointment itself is a constitutional mandate.