The correct option is Giving the Union Parliament power to make laws on matters included in the State List.
Explanation
The Constitution of India vests certain special powers exclusively in the Rajya Sabha to uphold the federal character of the Indian polity. These powers allow the Council of States to protect the interests of the States against potential encroachment by the Union Centre.
- Giving the Union Parliament power to make laws o Under Article 249, the Rajya Sabha has the exclusive power to authorize the Parliament to make laws on a subject enumerated in the State List. If the Rajya Sabha passes a resolution by a majority of not less than two-thirds of the members present and voting, declaring that it is necessary in the national interest, the Parliament becomes empowered to legislate on that specific State subject.
- Initiating a motion of no-confidence against the Council of Ministers. is Incorrect: The Council of Ministers is collectively responsible to the Lok Sabha (Article 75). Therefore, a motion of no-confidence can only be introduced and passed in the Lok Sabha. The Rajya Sabha has no power to remove the Ministry from office.
- Approving the Proclamation of Emergency. is Incorrect: The Proclamation of Emergency (National, State, or Financial) must be approved by both Houses of Parliament. This is a co-equal power shared by the Rajya Sabha and the Lok Sabha.
- Electing the President and Vice President. is Incorrect: The election of the President and the Vice President involves the participation of members from both Houses of Parliament (and State Legislative Assemblies in the case of the President). This is not an exclusive power of the Rajya Sabha.
Key Takeaway: The Rajya Sabha possesses two primary exclusive powers: authorizing Parliament to legislate on State List subjects (Article 249) and authorizing the creation of new All-India Services (Article 312).