Option 1: The Rajya Sabha does have a role in the election of the Vice-President. The Vice-President is elected by an electoral college consisting of members of both the Rajya Sabha and the Lok Sabha.
Option 2: The Rajya Sabha does have a role in the election of the Speaker. The Speaker of the Lok Sabha is elected from among its members, and both the Rajya Sabha and the Lok Sabha participate in the election process.
Option 3: The Rajya Sabha does have a role in the impeachment of the President. The President can be impeached by a special majority of both the Rajya Sabha and the Lok Sabha.
Option 4: The Rajya Sabha does have a role in the removal of judges of the Supreme Court. The process for the removal of judges requires an impeachment motion to be passed by a special majority of both the Rajya Sabha and the Lok Sabha.
Alert - correct answer should be 3: The Rajya Sabha has no role in the impeachment of the President. The impeachment process can only be initiated in the Lok Sabha, and the Rajya Sabha is not involved in this process.