Explanation:
The correct answer is option 'D' - H.P Blavatsky.

The Home Rule Leagues were political organizations that were formed in India during the early 20th century with the aim of advocating for self-government or home rule for India within the British Empire. These leagues played a significant role in the Indian independence movement.

Home Rule Leagues and their leaders:

a) Annie Besant: Annie Besant was a prominent British socialist, women's rights activist, and theosophist who played a vital role in the Indian national movement. She founded the Home Rule League in Madras (now Chennai) in 1916 and later in other parts of India. She advocated for self-government for India and worked towards promoting Indian culture and education. Besant played a significant role in mobilizing public support for the Indian independence movement.

b) Bal Gangadhar Tilak: Bal Gangadhar Tilak was an Indian nationalist, social reformer, and freedom fighter who is often referred to as the "Father of Indian Unrest." He was a strong advocate for Swaraj or self-rule and played a crucial role in the Indian independence movement. Tilak founded the Home Rule League in Maharashtra in 1916, which aimed at achieving self-government for India.

c) Joseph Baptista: Joseph Baptista was an Indian lawyer and politician who actively participated in the Indian freedom struggle. He was a key leader in the Home Rule Movement in Bombay (now Mumbai). Baptista was associated with the Bombay Home Rule League, which was formed in 1916 to demand self-government for India.

d) H.P Blavatsky: H.P Blavatsky was a Russian theosophist, writer, and occultist. She was not associated with the Home Rule Leagues in India. Blavatsky founded the Theosophical Society in 1875, which aimed at promoting spiritual knowledge and understanding.

Therefore, the correct answer is option 'D' - H.P Blavatsky.