The Panchayati Raj System, which is a system of local self-government in India, was introduced in the country in the year 1950 A.D. This system was implemented with the aim of decentralizing power and ensuring effective governance at the grassroots level. Option 1 is the correct answer.
Option 2, 1945 A.D., is incorrect as the Panchayati Raj System was not introduced in India during this year.
Option 3, 1947 A.D., is also incorrect as the Panchayati Raj System was not implemented immediately after India gained independence in 1947.
Option 4, 1962 A.D., is incorrect as the Panchayati Raj System was introduced in India prior to this year.
Therefore, the correct answer is option 1, 1950 A.D.