Among the given options, the river that does not flow into the Bay of Bengal is option 3, Tapti.

1. Mahanadi: This river flows through the states of Chhattisgarh and Odisha, and finally empties into the Bay of Bengal.

2. Cauvery: This river flows through the states of Karnataka and Tamil Nadu, and ultimately drains into the Bay of Bengal.

3. Tapti: This river, also known as Tapi, flows through the states of Maharashtra, Gujarat, and Madhya Pradesh. However, it does not empty into the Bay of Bengal. Instead, the Tapti river drains into the Arabian Sea.

4. Godavari: This river is the second-longest river in India and flows through the states of Maharashtra, Telangana, Andhra Pradesh, Odisha, and finally empties into the Bay of Bengal.

Therefore, based on this information, the correct answer is option 3, Tapti, as it does not flow into the Bay of Bengal.

Alert - correct answer should be Tapti Drains into Arabian Sea.