Consider the following statements:
1. The Executive Power of the Union of India is vested in the Prime Minister.
2. The Prime Minister is the ex officio Chairman of the Civil Services Board.
Which of the statements given above is/are correct?

The correct option is Neither 1 nor 2.

Let us analyze each statement step-by-step to understand why they are incorrect:

Analysis of Statement 1: "The Executive Power of the Union of India is vested in the Prime Minister."
According to Article 53(1) of the Constitution of India, the executive power of the Union is formally vested in the President of India, not the Prime Minister. The Article states that this power shall be exercised by the President either directly or through officers subordinate to him in accordance with the Constitution. While the Prime Minister is the real executive authority (de facto head of government), the President is the constitutional or formal head of the state (de jure head). Therefore, Statement 1 is incorrect.

Analysis of Statement 2: "The Prime Minister is the ex officio Chairman of the Civil Services Board."
The Civil Services Board, which recommends transfer and postings of civil servants, is chaired by the Cabinet Secretary of India, who acts as its ex officio Chairman. The Prime Minister is not the Chairman of this board. Therefore, Statement 2 is also incorrect.

Since both Statement 1 and Statement 2 are incorrect, the correct option is "Neither 1 nor 2".