The correct answer is option 1, the First Administrative Reforms Committee. The First Administrative Reforms Committee was established in 1966 by the Government of India to examine the state of administration in the country and suggest reforms. One of the recommendations made by this committee was the establishment of the Institutions of Lokpal and Lokayukta.

Option 2, the Gorwala Report, is incorrect. The Gorwala Report, also known as the Report on Public Administration, was published in 1951 and focused on improving the efficiency and effectiveness of government administration.

Option 3, the Ashok Mehta Committee, is incorrect. The Ashok Mehta Committee was appointed in 1977 to recommend constitutional reforms.

Option 4, the Appleby Reports, is incorrect. There is no known reference to the Appleby Reports in the context of the establishment of the Institutions of Lokpal and Lokayukta.

Therefore, the correct answer is option 1, the First Administrative Reforms Committee.