Prime Minister:

The Prime Minister of India is the head of government of the Republic of India, and head of the Council of Ministers, appointed by the President to assist the latter in the administration of the affairs of the executive in India. The Prime Minister is responsible for the discharge of the functions and power vested in the President in terms of the Constitution of India. He is appointed by the President, being recognized as the leader of the majority party in the two Houses of the Parliament of India.
The Constitution envisages a scheme of affairs in which the President of India is technically the head of the executive in terms of Article 53 with office of the Prime Minister as heading the Council of Ministers to assist and advise the President in the discharge of the executive power. To quote, Article 53 and 74 provide as under;
The Prime Minister leads the functioning and exercise of authority of the Government of India. He or she is invited by the President as leader of the majority party in the Parliament of India to form a government at the federal level (known as Central Government in India) and exercise its powers.
In practice the Prime Minister nominates the members of his or her Council of Ministers [1] [2] [3] to the President. He or she also works upon to decide a core group of Ministers (known as the Cabinet)[1] as in-charge of the important functions and ministries of the Government of India.