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The first statement is incorrect because the sources of the rivers Teesta and Brahmaputra are not the same. River Teesta originates from the Pahunri (Teesta Kangse) Glacier in Sikkim, while the Brahmaputra originates from the Angsi Glacier in Tibet.
The second statement is correct. River Rangeet does indeed originate in Sikkim and it is a significant tributary of the Teesta River, joining it at the confluence near Teesta Bazaar.
The third statement is incorrect. Although the Teesta River does flow into the Bay of Bengal, it doesn`t do so at the border of India and Bangladesh but rather within Bangladesh itself. Before reaching the Bay of Bengal, the river merges with the Brahmaputra (or Jamuna) in Bangladesh. Hence, the correct answer is option 2 - 2 only.