The Governor of a state may exercise discretionary powers when 1. he or she is not convinced by the advice of the Council of Ministers 2. the Constitution requires him/her to act in his/her discretion in certain matters 3. he or she is appointed as the administrator of an adjoining Union Territory Select the correct answer using the code given below:

Under Article 163 of the Constitution, the Governor acts on the aid and advice of the Council of Ministers except in matters where the Constitution requires him to act in his discretion [2]. Statement 1 is incorrect because the Governor cannot exercise discretion simply by being 'unconvinced' by advice; he is generally bound by it unless a constitutional provision specifies otherwise. Statement 2 is correct as Article 163(1) explicitly recognizes discretionary powers 'by or under' the Constitution. Statement 3 is correct because when a Governor is appointed as the administrator of an adjoining Union Territory under Article 239(2), he exercises his functions as such administrator independently of his state Council of Ministers. Thus, only statements 2 and 3 represent valid instances of discretionary or independent action.

Sources

1. [1] Indian Polity, M. Laxmikanth(7th ed.) > Chapter 30: Governor > CONSTITUTIONAL POSITION OF GOVERNOR > p. 321
2. [2] Laxmikanth, M. Indian Polity. 7th ed., McGraw Hill. > Chapter 30: Governor > CONSTITUTIONAL POSITION OF GOVERNOR > p. 321