Explanation:

- Option 1: Krishna

- The Krishna River does not originate at Trimbakeshwar.

- It begins in the Western Ghats at Mahabaleshwar in Maharashtra.

- Option 2: Damodar

- The Damodar River starts in the Chota Nagpur Plateau of Jharkhand.

- It is not related to Trimbakeshwar.

- Option 3: Godavari

- The Godavari River originates at Trimbakeshwar in Maharashtra.

- It is known as the second longest river in India.

- Option 4: Mahanadi

- The Mahanadi River originates from the Sihawa hills in Chhattisgarh.

- It does not start at Trimbakeshwar.