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Option 1: One year is incorrect. This is because the maximum time a person can continue to be the minister of the State Government without being a member of the state legislature is not one year.
Option 2: Three months is incorrect. This is because the maximum time a person can continue to be the minister of the State Government without being a member of the state legislature is not three months.
Option 4: No time limit is incorrect. This is because there is a time limit for a person to continue as a minister without being a member of the state legislature.
Therefore, option 3: Six months is the correct answer. This means that a person can only serve as a minister of the State Government without being a member of the state legislature for a maximum period of six months.