The correct answer is (d) Six months.
A person can remain a member of the Council of Ministers without being a member of the Parliament for a maximum period of six months. This is because the Constitution of India states that a person can only be a minister for six months without being a member of either House of Parliament. After six months, the person must either get elected to Parliament or resign from the Council of Ministers.
The other options are incorrect because they are not mentioned in the Constitution of India.