The correct answer is option 1, which states that only statement 1 is correct. Let`s analyze each statement to understand why.

Statement 1: No money bill can be introduced in the Parliament without the recommendation of the President of India. This statement is correct. According to Article 117 of the Indian Constitution, a money bill can only be introduced in the Parliament with the prior recommendation of the President. The President`s recommendation is required because money bills deal with matters related to taxation, government spending, borrowing, and lending of money by the government.

Statement 2: The Prime Minister appoints the Finance Commission for the distribution of taxes between the Union and the States. This statement is incorrect. The Finance Commission is actually appointed by the President of India, not the Prime Minister. The Finance Commission is a constitutional body set up under Article 280 of the Indian Constitution. Its primary responsibility is to recommend the distribution and allocation of taxes between the Union government and the State governments.

In conclusion, only statement 1 is correct, and the Prime Minister does not appoint the Finance Commission.