Indian Polity and Governance

The Chief Justice of India administers the oath of office to the President.

The Chief Executive authority of the Indian Union is the President of India.

The President of India has the power to appoint the Judges of the Supreme Court and the High Courts.

The President of India can declare war or conclude peace with any foreign power on the advice of the Council of Ministers.

Elected members of the Parliament participate in the election of the Vice President.

The Governor of the state being an agent of the Centre, takes over the administrative powers of the state into his hands.

Under Article 53 of the Indian Constitution, the Supreme Command of the Armed Forces is vested in the President of India. However, this power is exercised on the advice of the Union Cabinet (headed by the Prime Minister). The President is the ceremonial head while actual control is with the elected government.

The President can only be removed by impeachment under Article 61, requiring a charges resolution by 2/3 of Lok Sabha and investigation by Rajya Sabha, followed by a 2/3 vote of both Houses. Lok Sabha alone cannot remove the President (that's for the Prime Minister), and the President cannot be removed by the judiciary or Prime Minister.

The Attorney General of India can participate in Lok Sabha proceedings and speak but cannot vote. As the government's chief legal advisor, AG has right of audience in all Indian courts. The CEC, CAG, and Finance Commission Chair are statutory officials but do not have Lok Sabha participation rights.

The Prime Minister is a senior member of cabinet. The Prime Minister selects and can dismiss other members of the cabinet; allocates posts to members within the Government; is the presiding member and chairman of the cabinet; and is responsible for bringing a proposal of legislation.

The Chief Election Commissioner of India can be removed from office through the same impeachment process as a Supreme Court judge - by a two-thirds majority of Parliament membership on grounds of 'proved misbehavior or incapacity.' This ensures the CEC has security of tenure and independence similar to constitutional court judges. The CAG has similar removal provisions, while the Attorney-General and High Court judges have different removal procedures.

Option (1) is incorrect: A judge is a public officer under Section 2(17) of the CPC. Option (2) is incorrect: A person in service under the pay of government is a public officer under Section 2(17) of the CPC. Option (3) is correct: The Sarpanch of a gram panchayat is not a public officer under Section 2(17) of the CPC. Option (4) is incorrect. 

The Vice-President of India serves as the ex-officio Chairman of the Rajya Sabha and presides over its sessions. The Speaker presides over the Lok Sabha, while the Prime Minister and President do not preside over Rajya Sabha meetings.

According to Article 75(3) of the Indian Constitution, the Council of Ministers is collectively responsible to the Lok Sabha (House of the People). This means they must retain the confidence of the Lok Sabha majority. The President appoints the ministers but cannot remove them at will - only on the advice of the Prime Minister who has lost the Lok Sabha's confidence.