Statement 1 is incorrect. As per Article 53(1) of the Constitution of India, the executive power of the Union is vested in the President. The President exercises this power either directly or through officers subordinate to him in accordance with the Constitution. The Prime Minister, along with the Council of Ministers, aids and advises the President in the exercise of these functions.
Statement 2 is incorrect. The Cabinet Secretary is the ex-officio Chairman of the Civil Services Board. This board is responsible for recommendations regarding postings, transfers, and service matters of senior civil servants, particularly those belonging to the Indian Administrative Service (IAS).
Since both Statement 1 and Statement 2 are factually incorrect, option (d) is the correct answer.
Option (a) 1 only: This is incorrect because Statement 1 incorrectly attributes the executive power of the Union to the Prime Minister instead of the President.
Option (b) 2 only: This is incorrect because Statement 2 wrongly identifies the Prime Minister as the ex-officio Chairman of the Civil Services Board, a position held by the Cabinet Secretary.
Option (c) Both 1 & 2: This is incorrect as both statements provided in the question are factually inaccurate.