A person who is not a member of the state legislature can be appointed as…

Article 164(4) of the Constitution of India lays down that a person may be appointed a Minister of a State — an office that includes the Chief Minister, who heads the Council of Ministers — even though that person is not, at the time of appointment, a member of the State Legislature. Such a person, however, ceases to hold ministerial office on the expiry of six consecutive months from the date of appointment unless, before that period ends, they become a member of the Legislature (the Legislative Assembly, or the Legislative Council where the rules permit).

Applying this to the question: a person who is not a member of the state legislature can indeed be sworn in as Chief Minister, but the Constitution gives such a person only six consecutive months to secure membership of the Legislature. If they are not elected (or, where applicable, nominated) within that period, they automatically cease to be Chief Minister. The Supreme Court has affirmed that this six-month limit under Article 164(4) applies fully to the Chief Minister, since the Chief Minister is himself or herself a Minister within the meaning of that clause, with no separate or extended limit for the office.

Checking this against the given options:

• 2 months and 4 months are both shorter than the period the Constitution actually allows, so they understate the window given by Article 164(4).

• 1 year is longer than the period the Constitution allows; Article 164(4) fixes the outer limit at six consecutive months, not twelve.

• Six months is the exact period fixed by Article 164(4), so it is the correct answer.