The correct answer is option 2 - To decide at his/her discretion any question regarding disqualification of a Member of Parliament.

Let`s dissect each option to understand why option 2 is the correct answer and why the other options are not correct:

Option 1 - Appointment of Prime Minister: The President of India does have the power to appoint the Prime Minister. This power is mentioned in Article 75(1) of the Indian Constitution, which states that the President shall appoint the Prime Minister who in his/her opinion is most likely to command the confidence of the majority in the Lok Sabha.

Option 3 - To grant pardon to a person punished by court-martial: The President of India does possess the power to grant pardon, reprieve, respite, or remission of punishment or to suspend, remit or commute the sentence of any person punished by a court-martial. This power is mentioned in Article 72 of the Indian Constitution.

Option 4 - To remove a Judge of the High Court: The President of India does not have the power to remove a Judge of the High Court. The power to appoint and remove judges of the High Courts is vested in the President, but only after consultation with the Chief Justice of India and the Governor of the State. The