Statement 1 is Incorrect: The executive power of the Union is vested in the President, who acts on the advice of the Council of Ministers headed by the Prime Minister. The Constitution of India vests the executive power in the President (Article 53). However, the President exercises this power on the advice of the Council of Ministers, with the Prime Minister as its head (Article 75). So, the real executive authority lies with the Prime Minister and the Council of Ministers, but formally it's vested in the President. Statement 2 is Incorrect: The Chairperson of the Civil Services Board is the Cabinet Secretary, a senior bureaucrat who leads the bureaucracy of the Government of India.