The Prime Minister of India, at the time of his/her appointment:

Need 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 months.
Need 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.
Must be a member of one of the Houses of the Parliament.
Must be a member of the Lok Sabha.

Answer

Need 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 months.

(a) Under Article 75(5), a minister who is not a member of either House for six consecutive months ceases to be a minister. Since the Prime Minister is also a minister, he/she may be appointed without being an MP initially, but must enter either House within six months. Verdict: Correct.
(b) The Constitution does not require the Prime Minister to become a member of the Lok Sabha specifically; membership of Rajya Sabha also suffices. Verdict: Incorrect.
(c) The Prime Minister need not already be a member of either House at the time of appointment; this can be regularized within six months. Verdict: Incorrect.
(d) There is no constitutional requirement that the Prime Minister must be a member of the Lok Sabha. Verdict: Incorrect.