The correct answer is option 1, B.C. Tilak.

B.C. Tilak played a crucial role in the formation of the Home Rule League in India. The Home Rule League was a political organization that aimed to attain self-government or "home rule" for India within the British Empire. It was formed in 1916, during the period of the Indian nationalist movement.

G.R. Gokhale, M.G. Ranade, and M.K. Gandhi were also important figures in the Indian freedom struggle, but they were not directly involved in forming the Home Rule League. G.R. Gokhale was a prominent leader who advocated for political reforms, while M.G. Ranade was a social reformer and co-founder of the Indian National Congress. M.K. Gandhi, also known as Mahatma Gandhi, emerged as a leader later and his approach to the freedom struggle differed from that of Tilak.

Therefore, the correct answer is B.C. Tilak, who formed the Home Rule League in India.