The correct answer is: A. One year
The Constitution of India does not provide any specific time limit for a person to continue to be a minister of the State Government without being a member of the state legislature. However, the Tenth Schedule to the Constitution, which deals with the Anti-Defection Law, provides that a member of a House of the State Legislature who is disqualified on the ground of defection shall not be eligible to hold any office of profit under the Government of the State until he has been re-elected to the House.
In view of this provision, it is generally understood that a person can continue to be a minister of the State Government without being a member of the state legislature for a maximum period of one year. This is because, if a person is not elected to the state legislature within one year of being disqualified on the ground of defection, he will automatically cease to be a minister.
However, there is no bar on a person being re-elected to the state legislature after being disqualified on the ground of defection. In such a case, the person will be eligible to hold any office of profit under the Government of the State.
The options B, C, and D are incorrect because they do not reflect the current position of law.