The Prime Minister of India, at the time of his/her appointment
- Aneed not necessarily be a member of one of the Houses of the Parliament but must become a member of one of the Houses within six monthsCorrect
- Bneed not necessarily be a member of one of the Houses of the Parliament but must become a member of the Lok Sabha within six months
- Cmust be a member of one of the Houses of the Parliament
- Dmust be a member of the Lok Sabha
Explanation
The Constitution of India does not require a person to be a member of either House of Parliament at the time of their appointment as Prime Minister. According to Article 75, a Minister who is not a member of either House for any period of six consecutive months shall cease to be a Minister.
The Supreme Court of India confirmed in 1997 that a person who is not a member of either House can be appointed as Prime Minister, provided they get elected to either the Lok Sabha or the Rajya Sabha within six months. While the Prime Minister is usually a member of the Lok Sabha, there is no constitutional bar against a member of the Rajya Sabha or even a non-member being appointed, as long as the six-month requirement is met. Therefore, option A is correct because it allows for membership in either House, whereas option B incorrectly restricts it only to the Lok Sabha.

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