The correct answer is option 1, All India Muslim Ladies Conference. Anjuman-e-Khawatin-e-Islam, founded in 1914, was an organization that focused on the welfare and empowerment of Muslim women in India. It was a platform for Muslim women to come together, discuss issues, and work towards their social and educational upliftment. The organization aimed to challenge societal norms and promote gender equality within the Muslim community.

Option 2, A radical wing of the All India Muslim League, is incorrect. Anjuman-e-Khawatin-e-Islam was not a radical wing of the All India Muslim League. It was an independent organization that specifically catered to Muslim women.

Option 3, All India Muslim Students` Conference, is also incorrect. Anjuman-e-Khawatin-e-Islam was focused on the welfare of Muslim women, not on the educational needs and interests of Muslim students.

Option 4, All India Islamic Conference, is also incorrect. Anjuman-e-Khawatin-e-Islam was specifically focused on addressing the issues faced by Muslim women, rather than being a general Islamic conference.

Therefore, the correct answer is option 1, All India Muslim Ladies Conference.