Explanation:

Explanation: 
In the scheme of parliamentary system of government provided by the constitution, the President is the nominal executive authority (de jure executive) and Prime Minister is the real executive authority (de facto executive). In other words, president is the
head of the State while Prime Minister is the head of the government.
Statements 1 is correct: The Constitution does not contain any specific procedure for the selection and appointment of the Prime Minister. Article 75 says only that the Prime Minister shall be appointed by the president. However, this does not imply that the president is free to appoint any one as the Prime Minister. In accordance with the conventions of the parliamentary system of government, the President has to appoint the leader of the majority party in the Lok Sabha as the Prime Minister. But, when no party has a clear majority in the Lok Sabha, then the President may exercise his personal discretion in the selection and appointment of the Prime Minister. In such a situation, the President usually appoints the leader of the largest party or coalition in the Lok Sabha as the Prime Minister and asks him to seek a vote of confidence in the House within a month. Constitutionally, the Prime Minister may be a member of any of the two Houses of parliament.
Statement 2 is not correct: In 1997, the Supreme Court held that a person who is not a member of either House of Parliament can be appointed as Prime Minister for six months, within which, he should become a member of either House of Parliament; otherwise, he ceases to be the Prime Minister.