who exercise the actual executive power under the parliamentary form of government
Prime minister The prime minister is often, but not always, a member of the Legislature or the Lower House thereof and is expected with other ministers to ensure the passage of bills through the legislature. In some monarchies the monarch may also exercise executive powers (known as the royal prerogative) that are constitutionally vested in the crown and may be exercised without the approval of parliament.
President of India Although the Article 53 of the Constitution of India states that the President can exercise his powers directly or by subordinate authority, with few exceptions, all of the executive powers vested in the President are, in practice, exercised by the Prime Minister (a subordinate authority) with the help of the Council of Ministers.[3] The President is bound by the constitution to act on the advice of the Prime Minister and Cabinet as long as the advice is not violating the constitution.