The correct answer to the question is option 4, Council of Ministers. In the Indian Republic, the real executive authority rests with the Council of Ministers. The Council of Ministers is a group of senior ministers chosen by the Prime Minister who are collectively responsible for the day-to-day administration of the government. They are appointed by the President of India on the advice of the Prime Minister. The Prime Minister, though an important figure, is not the real executive authority on their own. The President, on the other hand, holds a largely ceremonial position and acts on the advice of the Council of Ministers. Bureaucrats, though playing a crucial role in implementing policies, do not possess executive authority themselves but operate under the direction of the elected government.