The correct answer is option 1, Barak. Barak is not a desert river.

Let`s examine each of the options to understand why they may or may not be desert rivers:

1. Barak (not a desert river): Barak is a river located in northeastern India and Bangladesh. It flows through a region that is not classified as a desert.

2. Rupen (potentially a desert river): The Rupen river is located in Gujarat, India. Although Gujarat is known for its arid regions, it is not explicitly mentioned if the Rupen river flows through a desert or arid region.

3. Banas (potentially a desert river): The Banas river is a significant river in Rajasthan, India. Rajasthan is known for its Thar Desert, so it is plausible that the Banas river could flow through or have connections to desert areas.

4. Machchhu (potentially a desert river): Machchhu is a river that flows through the Saurashtra region in Gujarat, India. This region does have arid regions and semi-desert areas.

Based on the information provided, Barak is the only option that is not associated with desert or arid regions. Therefore, option 1 is the correct answer