The purpose with which Sir William Wedderburn and W.S. Caine had set up the Indian Parliamentary Committee in 1893 was to agitate for Indian political reforms in the House of Commons. Therefore, the correct answer is option A: "To agitate for Indian political reforms in the House of Commons."

The Indian Parliamentary Committee was established in London in 1893 by Wedderburn and Caine to create a platform for Indian nationalists to voice their concerns and lobby for political reforms in India. The committee consisted of British and Indian members and aimed to influence British public opinion and parliamentary debates on Indian issues. The committee was instrumental in highlighting the grievances of Indians and pressing for reforms such as greater Indian representation in the legislative councils, Indian control over the budget, and greater civil liberties for Indians.