Final answer:
The special power given to the Rajya Sabha by the Indian Constitution is to pass a resolution enabling the Parliament to legislate on matters in the State List and to create All India Services.
Step-by-step explanation:
The special power conferred on the Rajya Sabha by the Constitution of India is B) to pass a resolution empowering the Parliament to make laws in the State List and to create one or more All India Services. Unlike the U.S. Senate, which has powers such as ratifying treaties and confirming presidential appointments, the Rajya Sabha holds certain distinctive powers that pertain to India's federal structure and balance of powers between the Union and states.
The Rajya Sabha's role in the Indian legislative process includes powers that are not shared with the Lok Sabha, India's other parliamentary house. For example, under Article 249 of the Indian Constitution, the Rajya Sabha can pass a resolution by a two-thirds majority to enable the Parliament to make laws on a subject enumerated in the State List (which is normally within the purview of state legislatures) if it is deemed necessary in the national interest. Additionally, under Article 312, the Rajya Sabha can pass a resolution to create new All India Services, which then requires a subsequent law passed by Parliament.
The other options provided, such as the power to impeach the President, and the power to determine the functions of the Election Commission, are not within the Rajya Sabha's purview. The power to bifurcate an existing state is also not a direct function of Rajya Sabha, but rather it involves a constitutional amendment and ratification process that requires the participation of both houses of Parliament.