The correct answer is option 3, which states that the Narmada river is the only west-flowing river of India. Let`s dissect each option to understand why the answer is correct.

Option 1 includes the Mahanadi, Krishna, and Cauvery rivers. However, these rivers are not west-flowing rivers. The Mahanadi river flows in an eastward direction and empties into the Bay of Bengal. Similarly, the Krishna and Cauvery rivers also flow eastward and drain into the Bay of Bengal. Therefore, option 1 is incorrect.

Option 2 includes the Krishna and Narmada rivers. The Krishna river is not a west-flowing river; it flows eastward and drains into the Bay of Bengal. However, the Narmada river does flow westward and empties into the Arabian Sea. Therefore, option 2 is incorrect.

Option 3 correctly identifies the Narmada river as the only west-flowing river of India. Therefore, option 3 is the correct answer.

Option 4 includes the Mahanadi and Narmada rivers. As mentioned earlier, the Mahanadi river does not flow westward; it flows eastward and drains into the Bay of Bengal. Therefore, option 4 is incorrect