Explanation:

- Option 1: Chief Minister of the State

- The Chief Minister doesn't have the authority to appoint the Governor. They play a role at the state level but not in this appointment process.

- Option 2: Prime Minister

- The Prime Minister advises the President but does not directly appoint the Governor.

- Option 3: Chief Justice of the High Court

- The Chief Justice is responsible for judicial functions and has no role in appointing the Governor.

- Option 4: President

- The President of India appoints the Governor of a state, including Jammu and Kashmir. This power comes under the President's responsibilities in the Indian Constitution.