The Indian Home Rule League at Madras was founded by ______.

The correct answer is Annie Besant.

Step-by-step Explanation:

1. Understanding the Home Rule Movement:
The Home Rule Movement in India was a prominent campaign in the Indian independence movement, modeled on the Irish Home Rule league. Its primary objective was to achieve self-government (home rule) for India within the British Empire.

2. Two Different Leagues:
Two separate Home Rule Leagues were established to carry out this movement:
- Bal Gangadhar Tilak launched the first league in April 1916 at Belgaum, targeting Maharashtra (excluding Bombay), Karnataka, the Central Provinces, and Berar.
- Annie Besant, an Irish socialist, activist, and writer, launched her own league in September 1916 at Madras (now Chennai) to cover the rest of India, including Madras Presidency.

3. The Indian Home Rule League at Madras:
Because Annie Besant set up her headquarters and initiated her league in Madras, the Indian Home Rule League at Madras is directly associated with her leadership and founding efforts.