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

The correct answer is option 1) Annie Besant.

Important Points

•  Annie Besant, a prominent British theosophist, social reformer, and Indian nationalist, established the Central Hindu Girls' School in Varanasi (formerly known as Banaras) in 1904
• to provide modern, western-style education to girls in India.
• The school was established with the support of the Indian nationalist leader, Bal Gangadhar Tilak, and the Benares Hindu University.
• The school became a model for girls' education in India, and it helped to break down traditional barriers to women's education in the country.
• Besant was a strong advocate for women's education and played a significant role in the establishment of several other educational institutions for women in India, including the
  • Besant Theosophical College in Chennai
  • the National Girls' School in Calcutta​
• Annie Besant first visited India in 1893 and later settled there, becoming involved in the Indian nationalist movement.
• In 1916 she established the Indian Home Rule League, of which she became president.
• She was also a leading member of the Indian National Congress.
• As a member and later leader of the Theosophical Society, Besant helped spread Theosophical beliefs worldwide.
• Annie Besant founded two newspapers. The first one was a weekly newspaper titled "The Commonweal" and the second one was "New India"