The correct answer is: B. on the recommendation of the prime minister.
The President of India can dismiss a member of the Council of Ministers only on the recommendation of the Prime Minister. This is because the Prime Minister is the head of the Council of Ministers and is responsible for the appointment and dismissal of its members. The President is bound by the advice of the Prime Minister in this matter.
Option A is incorrect because the President cannot dismiss a member of the Council of Ministers on his own. The President can only dismiss a member of the Council of Ministers on the recommendation of the Prime Minister.
Option C is incorrect because the President can dismiss a member of the Council of Ministers even if there is no emergency. The President can dismiss a member of the Council
of Ministers on the recommendation of the Prime Minister at any time.Option D is incorrect because the President does not need the consent of the Speaker to dismiss a member of the Council of Ministers. The President can dismiss a member of the Council of Ministers on the recommendation of the Prime Minister without the consent of the Speaker.