Option 1 -> Subramania Bharati was a poet and political activist, not the founder of the Theosophical Society.
Option 2 -> Sri Aurobindo was a spiritual leader whom Bharati met in Pondicherry in 1910, not the founder of the Theosophical Society.
Option 3 -> Annie Besant is explicitly mentioned in the passage as "a political activist and the founder of the Theosophical Society of India."
Option 4 -> Sister Nivedita was a disciple of Swami Vivekananda who influenced Bharati, but not the founder of the Theosophical Society.
Hence, Option 3: Annie Besant -> The passage clearly states that Bharati attended lectures by Annie Besant in Banaras, describing her as "a political activist and the founder of the Theosophical Society of India" -> correct