The correct answer to the question is option 1, which states that all three statements are correct.

Let`s analyze each statement to understand why it is correct:

1. When the Governor is not convinced by the advice of the Council of Ministers:

Discretionary powers allow the Governor to make decisions independently, without being bound by the advice of the Council of Ministers. This means that even if the Council of Ministers suggests a course of action, the Governor can use their discretionary powers to make a different decision if they are not convinced by the advice given.

2. When the Constitution requires the Governor to act in his/her discretion in certain matters:

The Constitution of India grants discretionary powers to the Governor in certain situations. These situations are explicitly mentioned in the Constitution itself, and in such cases, the Governor is required to exercise their discretion while making decisions.

3. When the Governor is appointed as the administrator of an adjoining Union Territory:

When the Governor is appointed as the administrator of an adjoining Union Territory, they are given discretionary powers to carry out their duties effectively. These powers allow them to make decisions on behalf of the Union Territory autonomously, without always requiring the advice or approval of the Council of Ministers.

In conclusion, all three statements accurately describe situations in which the