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?

Let's analyze the given statements:

1. The Executive Power of the Union of India is vested in the Prime Minister: This statement is incorrect. According to Article 53(1) of the Indian Constitution, the executive power of the Union is vested in the President and shall be exercised by him either directly or through officers subordinate to him in accordance with this Constitution. While the Prime Minister is the real executive head and exercises most of the executive powers in practice, the formal and constitutional vesting of executive power is in the President.

2. The Prime Minister is the ex officio Chairman of the Civil Services Board: This statement is incorrect. The Civil Services Board is typically chaired by the Cabinet Secretary, who is the senior-most civil servant in India. The Prime Minister is the head of the government and the political executive, but not the ex-officio chairman of the Civil Services Board.

Therefore, neither statement 1 nor statement 2 is correct.