Correct Option
The Prime Minister of India can be a member of either the Lok Sabha or the Rajya Sabha, as per Article 75 of the Constitution. A no-confidence motion can only be introduced and passed in the Lok Sabha, as it is the directly elected House to which the Council of Ministers is collectively responsible. If the Prime Minister is a member of the Rajya Sabha, they are entitled to attend and participate in the proceedings of the Lok Sabha. However, the right to vote in a House is restricted to its members. Consequently, a Prime Minister from the Rajya Sabha cannot cast a vote in the Lok Sabha, including during a no-confidence motion, even though the outcome directly affects their government's tenure.
Incorrect Options
A Prime Minister who is a member of the Rajya Sabha is permitted to attend and speak in the Lok Sabha. This includes participating in discussions on the budget, subject to the Speaker's permission. Therefore, the statement that they cannot speak on the budget in the Lower House is incorrect.
The Prime Minister, irrespective of their House membership, is not restricted to making statements only in the Upper House (Rajya Sabha). They can make statements in either House of Parliament as required. Hence, this statement is incorrect.
The requirement to become a member of Parliament within six months applies to individuals who are appointed as ministers (including the Prime Minister) without being a member of either House at the time of their appointment. If the Prime Minister is already a member of the Rajya Sabha, they fulfill the constitutional requirement of being a Member of Parliament and are not obligated to become a member of the Lok Sabha. Therefore, this statement is incorrect.