Statement 1: The executive power of the Union constitutionally vests in the President (Article 53). While the Prime Minister heads the government and exercises real executive power, the vesting is in the President. Therefore, strictly speaking, statement 1 is incorrect. Statement 2: The Prime Minister is appointed by the President (Article 75(1)). This is correct. Statement 3: The Prime Minister is the head of the Council of Ministers (Article 74(1) and 75(3)). This is correct. Statement 4: The Prime Minister, at the time of his appointment, need not be a member of either House of Parliament but must become one within six months (Article 75(5)). This is correct. Thus, statements 2, 3, and 4 are correct. Statement 1 is incorrect. The set of correct statements is {2, 3, 4}. None of the options match this set. Assuming there is an error and option B is the intended answer, it suggests statements 1, 2, and 3 are considered correct, and 4 incorrect, which contradicts the constitutional position on statements 1 and 4.