Panchayati Raj was first introduced in India in October, 1959 in

Rajasthan was the first state to establish the modern Panchayati Raj system in India; the scheme was formally inaugurated by the Prime Minister on 2 October 1959 in Nagaur district of Rajasthan, marking the first implementation of the recommendations that led to Panchayati Raj institutions [1]. The Balwantrai G. Mehta Committee had earlier recommended the three-tier Panchayati Raj model (village gram panchayat, block-level panchayat samiti, and district zila parishad), which provided the framework for these state-level adoptions [2]. Andhra Pradesh adopted the system later in 1959, and most other states followed in the 1960s with variations in tiers and functions [1]. Hence, Rajasthan (option 1) is correct.

Sources

1. [1] Indian Polity, M. Laxmikanth(7th ed.) > Chapter 39: Panchayati Raj > Balwant rai Mehta Committee > p. 384
2. [2] Indian Polity, M. Laxmikanth(7th ed.) > Chapter 39: Panchayati Raj > Balwant rai Mehta Committee > p. 383