Explanation:

Only statements 1&3 are correct.

• Statement 1st is correct: Arvind Panagariya, the former Chairman of NITI Aayog, has indeed been appointed as the head of the 16th Finance Commission.

• Statement 2nd is incorrect: The Finance Commission is a constitutional body, not a statutory body, and is constituted under Article 280 of the Indian Constitution.

• Statement 3rd is correct: The primary objective of the Finance Commission is to address the distribution of financial resources between the Centre and the States.

Supplementary Notes

• The Finance Commission is constituted every five years or at such intervals as deemed necessary by the President.

• Its functions include recommending the distribution of net proceeds of taxes, principles governing grants-in-aid to States, and evaluating the impact of the Centre's debt on the fiscal autonomy of States.

• Arvind Panagariya's expertise as the head of the Finance Commission is expected to contribute to shaping India's financial landscape.

Hence option 2nd is correct.