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Option 1: "Pingali Venkayya designed the tricolour Indian National Flag here." This option is incorrect. Pingali Venkayya is indeed the designer of the Indian National Flag, but he designed it in Bezwada (now Vijayawada) in Andhra Pradesh. Madanapalle is not associated with the design of the Indian National Flag.
Option 2: "Pattabhi Sitaramaiah led the Quit India Movement of Andhra region from here." This option is also incorrect. While Pattabhi Sitaramaiah was a prominent Indian freedom fighter from Andhra Pradesh and played a key role in the Quit India Movement, he did not lead the movement in the Andhra region from Madanapalle.
Option 3: "Rabindranath Tagore translated the National Anthem from Bengali to English here." This option is incorrect. Rabindranath Tagore did translate the National Anthem of India from Bengali to English, but he did not do it in Madanapalle. The translation was done in Calcutta (now Kolkata).
Option 4: "Madame Blavatsky and Colonel Olcott set up headquarters of Theosophical Society first here." This option is correct. Madame Blavatsky and Colonel Olcott did establish the headquarters of Theosophical Society in Madanapalle in 1882. The Theosophical Society was founded in New York in 1875, and it established its first permanent headquarters in Madanapalle.