Explanation:

- Option 1: Sharavati

- Flows in Karnataka.

- Not between two mountain ranges.

- Option 2: Narmada

- Flows between the Vindhya and Satpura ranges.

- Drains into the Arabian Sea.

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- Option 3: Mahi

- Flows in India but not specifically between two mountain ranges.

- Option 4: Sabarmati

- Flows in Gujarat and Rajasthan.

- Not between two mountain ranges.

The Narmada River uniquely flows westward between the Vindhya and Satpura mountain ranges, making it the correct option.