Option 1: Madame H. P. Blavatsky - Madame H. P. Blavatsky was one of the co-founders of the Theosophical Society and played a major role in its activities. She was known for her writings on spiritualism and occultism.

Option 2: Mr. A. O. Hume - This option is the correct answer. Mr. A. O. Hume was not associated with the activities of the Theosophical Society. He was actually a key figure in the Indian National Congress and played a significant role in the Indian independence movement.

Option 3: Col. H. S. Olcott - Col. H. S. Olcott was one of the co-founders of the Theosophical Society along with Madame Blavatsky. He was involved in various activities of the society and played a crucial role in its growth and development.

Option 4: Mrs. Annie Besant - Mrs. Annie Besant was a prominent member of the Theosophical Society and succeeded Col. Olcott as its president. She actively participated in the activities of the society and worked towards spreading its teachings and philosophies.

In conclusion, option 2 (Mr. A. O. Hume) is the correct