President, Vice-President, and the Prime Minister-led Council of Ministers β who holds power, and who actually uses it.
The President is the constitutional (nominal) head of the Union executive. All executive power is formally vested in the President, but it is exercised on the "aid and advice" of the Council of Ministers β made binding in most cases by the 42nd and 44th Amendments to Article 74.
The President is elected by an Electoral College consisting of elected members of both Houses of Parliament and elected members of State (and, since 2019, Union Territory) Legislative Assemblies, using a system of proportional representation by single transferable vote. The term is 5 years, and removal is only by impeachment (Article 61) for violation of the Constitution.
The Vice-President is the ex-officio Chairman of the Rajya Sabha and acts as President if the office falls vacant. Elected by members of both Houses of Parliament (not state legislatures) via proportional representation.
The real executive power lies with the Council of Ministers, headed by the Prime Minister, who is appointed by the President and is usually the leader of the majority party/coalition in the Lok Sabha. The Council of Ministers is collectively responsible to the Lok Sabha (Article 75(3)) β meaning if the Lok Sabha loses confidence in the government, the entire Council must resign, not just individual ministers.
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