The given question asks us to identify the pair of a river and its tributary that is not correctly matched.
Option 1 states that Godavari is tributary to Wainganga. This is incorrect. In reality, Wainganga is a tributary of Godavari. A tributary is a smaller river or stream that flows into a larger river, and in this case, Wainganga flows into Godavari.
Option 2 states that Cauvery is tributary to Bhavani. This is correct. Bhavani is one of the main tributaries of the Cauvery river in the southern part of India.
Option 3 states that Narmada is tributary to Amaravati. This is incorrect. Narmada is one of the major rivers in central India and Amaravati does not flow into it.
Option 4 states that Krishna is tributary to Bhima. This is correct. Bhima is one of the main tributaries of the Krishna river in western India.
In conclusion, option 3 is the correct answer since Narmada and Amaravati are not a pair of a river and its tributary.