The correct answer is option 3: Appointed by the President. The Prime Minister of India is not elected by the Lok Sabha or the Parliament. Rather, the President of India appoints the Prime Minister.

The President`s appointment follows a process where the political party or coalition of parties that has the majority in the Lok Sabha recommends a candidate for the position of Prime Minister. The President then appoints that candidate as the Prime Minister, who is responsible for forming the government and selecting other members of the Council of Ministers.

It is important to note that the Prime Minister holds a significant position in the Indian government and plays a crucial role in governance and decision-making. Their appointment by the President highlights the importance of the executive branch`s involvement in the selection of the Prime Minister.