The correct answer is option 2: Appointed. The Prime Minister of India is not elected directly by the people or nominated by any specific group. Instead, the President of India, who is the head of state, appoints the Prime Minister. The President usually appoints the leader of the political party or alliance that has the majority of seats in the lower house of Parliament, known as the Lok Sabha. The President`s decision is based on parliamentary conventions and recommendations from various political parties. Once the Prime Minister is appointed, they form a council of ministers to assist in the governance of the country. It is important to note that while the Prime Minister is appointed, they still require the support and confidence of the majority of members in the Lok Sabha to remain in power.