The correct option is 1 and 2 only.
Explanation
The Union Public Service Commission (UPSC) is the central recruiting agency in India. It is an independent constitutional body established under Article 315 of the Constitution (Part XIV) to ensure a merit-based selection system for the civil services.
Statement 1 is Correct: The Chairman and other members of the UPSC are appointed by the President. They hold office for a term of six years or until they attain the age of 65 years, whichever is earlier. This fixed tenure ensures their independence.
Statement 2 is Correct: Under Article 320, the primary function of the UPSC is to conduct examinations for appointments to the services of the Union. It is also consulted on matters relating to methods of recruitment and disciplinary matters affecting civil servants.
Statement 3 is Incorrect: The removal of a UPSC member is governed by Article 317. The President can remove a member for "misbehaviour" only after the Supreme Court has held an inquiry and reported that the member ought to be removed. While the President can remove a member without an inquiry on specific objective grounds (insolvency, engaging in paid employment outside duties, or infirmity of mind/body), the statement suggests a general power to remove without inquiry. This contradicts the constitutional safeguard of a mandatory Supreme Court inquiry for removal on the grounds of misbehaviour.
Key Takeaway: The independence of the UPSC is secured by the Constitution through a fixed tenure for its members and a rigorous removal procedure that, for cases of misbehaviour, requires a mandatory inquiry by the Supreme Court.