Explanation:

- Statement 1: The Governor cannot generally exercise discretionary power just because he/she is not convinced by the Council of Ministers. The Constitution expects the Governor to act on their advice, except in rare situations.

- Statement 2: The Constitution does require the Governor to act in his/her discretion in certain matters (e.g., reservation of a bill for the President, appointment of the Chief Minister when no party has a majority).

- Statement 3: If the Governor is appointed as the administrator of an adjoining Union Territory, he/she can act at his/her discretion regarding that territory.

Option 2 (1 and 2 only)

Option 3 (2 and 3 only)

Option 4 (3 only)

So, the correct answer is Option 3: 2 and 3 only.