Which one of the following statements is correct?

Statement 3 is correct because the Constitution of India does not prescribe a specific procedure or grounds for the removal of a Governor. Under Article 156, the Governor holds office during the pleasure of the President. Statement 1 is incorrect as the 7th Constitutional Amendment Act of 1956 allows the same person to be appointed as Governor for two or more states. Statement 2 is incorrect because High Court judges are appointed by the President, not the Governor, although the Governor is consulted [4]. Statement 4 is incorrect because in Union Territories with a legislative setup (like Delhi or Puducherry), the Chief Minister is appointed by the President, not the Lieutenant Governor. While the Governor appoints the Chief Minister in States [3], the specific constitutional provisions for Union Territories (e.g., Article 239AA) vest the appointment power in the President.

Sources

1. [4] Introduction to the Constitution of India, D. D. Basu (26th ed.). > Chapter 13: The State Executive > Powers of the Governor. The Governor has no diplomatic or military powers like the President, but he possesses executive, legislative and judicial powers analogous to those of the President. > p. 272
2. [1] Indian Polity, M. Laxmikanth(7th ed.) > Chapter 31: Chief Minister > APPOINTMENT OF CHIEF MINISTER > p. 325
3. [2] Laxmikanth, M. Indian Polity. 7th ed., McGraw Hill. > Chapter 31: Chief Minister > APPOINTMENT OF CHIEF MINISTER > p. 325
4. [3] Introduction to the Constitution of India, D. D. Basu (26th ed.). > Chapter 13: The State Executive > THE STATE EXECUTIVE > p. 273