The correct option "Neither 1 nor 2" is accurate because the Executive Power of the Union of India is vested in the President, not directly in the Prime Minister, although the President exercises this power on the advice of the Prime Minister and the Council of Ministers. Additionally, the Prime Minister is not the ex officio Chairman of the Civil Services Board; this role is typically held by the Cabinet Secretary. Understanding these distinctions is crucial for UPSC Prelims, as they reflect the constitutional framework and the separation of powers inherent in Indian governance.