Who among the following established the central Hindu Girl's School at Banaras with the object of western education to girls?

The correct option is Annie Besant.

Step-by-step Explanation:

1. Context and Foundation: Annie Besant, a prominent British socialist, theosophist, and women's rights activist, played a pivotal role in the Indian nationalist movement and social reforms. She arrived in India in 1893 and dedicated herself to the cause of education and societal advancement.
2. Establishment of the Central Hindu College: In 1898, Annie Besant founded the Central Hindu College (CHC) in Banaras (now Varanasi) to provide a synthesis of modern Western education and traditional Indian cultural values.
3. Focus on Women's Education: Understanding that the education of girls was crucial for the progress of Indian society, Annie Besant went on to establish the Central Hindu Girl's School at Banaras in 1904. The primary objective of the school was to impart modern Western scientific and literary education to girls while keeping them rooted in their cultural heritage.
4. Later Developments: The Central Hindu College and the Girls' School later became the nucleus for the establishment of the Banaras Hindu University (BHU) by Pandit Madan Mohan Malaviya in 1916.