The correct answer is (a).
When a Central Council of Ministers resigns, the President may ask them to continue in office until an alternative arrangement is made. This is usually done when there is a delay in forming a new government, such as after a general election. The President may also ask the outgoing Council of Ministers to continue in office if there is a national emergency.
Alternative arrangement does not mean that President’s rule will be imposed. President’s rule is a constitutional provision that allows the President to rule a state directly, without an elected government. This can only be done if the President is satisfied that a state government cannot be carried on in accordance with the provisions of the Constitution.
Outgoing Council of Ministers may have to hold charge till the formation of new Government. This is because the President cannot appoint a new Council of Ministers until the results of a general election are known. In the meantime, the outgoing Council of Ministers continues to hold office as a caretaker government.