how are the executive and legislative powers of a state exercised during the president rule
Answers
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.[2] 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.
When a state government is functioning correctly, it is run by an elected Council of Ministers responsible to the state's legislative assembly (Vidhan Sabha). The council is led by the Chief Minister, who is the de facto chief executive of the state; the Governor is only a de jure constitutional head. However, during President's rule, the Council of Ministers is dissolved, vacating the office of Chief Minister. Furthermore, the Vidhan Sabha is either prorogued or dissolved, necessitating a new election.