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Option 1: Penneru
The origin of the Penneru river is not in the Brahmagir range of Western Ghats. It actually originates from the Nandi Hills in the Chikkaballapur district of Karnataka. Therefore, option 1 is not correct.
Option 2: Kaveri
The Kaveri river is the correct answer. It originates in the Brahmagir range of the Western Ghats in Karnataka. It then flows through Tamil Nadu and eventually empties into the Bay of Bengal. Therefore, option 2 is correct.
Option 3: Krishna
The origin of the Krishna river is not in the Brahmagir range of Western Ghats. It actually originates in the state of Maharashtra, near the town of Mahabaleshwar. Therefore, option 3 is not correct.
Option 4: Tapti
The origin of the Tapti river is not in the Brahmagir range of Western Ghats. It actually originates in the Betul district of Madhya Pradesh. Therefore, option 4 is not correct.
In conclusion, the correct answer is option 2, Kaveri, as it is the only river that originates in the Brahmagir range of Western Ghats.