The Royal Commission on the Public Services in India was formed in 1912 to examine and make recommendations on the structure and organization of the public services in India. The correct answer to the question is option 4, Bal Gangadhar Tilak.
Option 1, Gopal Krishna Gokhale, was a prominent Indian nationalist leader and social reformer who was actively involved in the Indian political scene during that time. He was known for his advocacy of political reforms and his efforts towards achieving self-rule for India.
Option 2, Valence Chirol, was a British journalist and diplomat who had expertise in Indian affairs. He was appointed as a member of the Royal Commission to provide his insights and knowledge on the Indian public services.
Option 3, Abdur Rahim, was an Indian civil servant and a member of the Indian Civil Service. He was actively involved in administrative reforms and played a significant role in the Indian public services.
Based on the information provided, it can be concluded that Bal Gangadhar Tilak was not a member of the Royal Commission on the Public Services in India in 1912.