For how many months can a person be appointed Chief Minister without membership of the state legislature?

Correct option is A

The correct answer is(a) : 6 months.

Explanation:
6 months : According to the Indian Constitution, if a person is appointed as the Chief Minister of a state and is not already a member of the state legislature (either the Legislative Assembly or the Legislative Council), they must become a member of the legislature within 6 months of their appointment. If they fail to do so, they will cease to hold the office of Chief Minister. This is specified in Article 164(4) of the Constitution.

Information Booster:

• The Indian Constitution mandates that any person who is appointed as the Chief Minister must be a member of either the Legislative Assembly or the Legislative Council of the state.
  
• If they are not a member, they must get elected within six months from the date of appointment.