Answer:

Background:
The Home Rule League was a political organization founded by Annie Besant in 1916. It aimed to promote self-government and Home Rule for India within the British Empire. The league gained significant support from various Indian political leaders, including some Muslim League leaders.

Explanation:
Among the options given, Muhammad Ali Jinnah was the Muslim League leader who joined the Home Rule League founded by Annie Besant.

Muhammad Ali Jinnah:
Muhammad Ali Jinnah, also known as Quaid-e-Azam (Great Leader), was one of the prominent leaders of the Indian National Congress and later the Muslim League. He was a lawyer by profession and played a crucial role in the struggle for India's independence.

Reasons for Joining the Home Rule League:
1. Support for Self-Government: Jinnah, like many other Indian leaders, believed in the idea of self-government and Home Rule for India. The Home Rule League was founded on these principles, making it an attractive platform for Jinnah to join.
2. Unity among Different Communities: Jinnah recognized the importance of unity among different communities in India. By joining the Home Rule League, he aimed to work with leaders from various backgrounds to achieve common goals.
3. Strengthening the Muslim League: Jinnah's decision to join the Home Rule League was part of his broader strategy to strengthen the Muslim League. By participating in a non-communal organization like the Home Rule League, he aimed to present the Muslim League as a progressive and inclusive political entity.

Impact of Jinnah's Decision:
Jinnah's decision to join the Home Rule League showcased his willingness to work with leaders from different backgrounds and his commitment to the cause of self-government. It also helped in building alliances and forging relationships with other prominent political figures of the time.

Conclusion:
In conclusion, Muhammad Ali Jinnah, a leader of the Muslim League, joined the Home Rule League founded by Annie Besant. His decision was motivated by a desire for self-government, unity among different communities, and strengthening the Muslim League. Jinnah's involvement in the Home Rule League had a significant impact on the Indian political landscape and laid the foundation for his future role in shaping the destiny of Pakistan.