Correct Option
As per Article 75(5) of the Constitution of India, a person appointed as Prime Minister need not be a member of either House of Parliament at the time of appointment. However, such a person must become a member of either the Lok Sabha or the Rajya Sabha within six months from the date of appointment. Failure to do so results in the cessation of their Prime Ministership. This constitutional provision also applies to other ministers.
Incorrect Options
Option (b) is incorrect. While a person appointed as Prime Minister must become a member of Parliament within six months, it is not exclusively required to be a member of the Lok Sabha. Membership of the Rajya Sabha is also permissible to fulfill this constitutional requirement.
Option (c) is incorrect. The Constitution does not mandate that the Prime Minister must already be a member of one of the Houses of Parliament at the time of appointment. The provision allows for a six-month period to acquire membership in either House.
Option (d) is incorrect. There is no constitutional requirement for the Prime Minister to be a member of the Lok Sabha. Several individuals who served as Prime Ministers, such as Indira Gandhi (initially) and Manmohan Singh, were members of the Rajya Sabha at the time of their appointment or during their tenure.