The correct answer is option C) Krishna-Tungabhadra doab.

The Raichur doab is a fertile region located between the Krishna and Tungabhadra rivers in southern India. It was a permanent bone of contention between the kingdoms of Vijayanagar and Bahmani during the medieval period.

The significance of the Raichur doab can be understood by examining the historical context of the Vijayanagar and Bahmani kingdoms.

1. Vijayanagar Kingdom:
- The Vijayanagar Empire was founded in 1336 by Harihara and Bukka, two brothers who were initially governors of the Kakatiya Empire.
- The empire reached its zenith under the rule of Krishnadevaraya (1509-1529) and became a major power in southern India.
- Vijayanagar had control over the fertile regions of the Krishna-Tungabhadra doab, which provided them with agricultural resources and revenue.

2. Bahmani Kingdom:
- The Bahmani Sultanate was established in 1347 by Alauddin Hasan Bahman Shah, a governor of the Delhi Sultanate.
- The sultanate was primarily located in the Deccan region and had its capital at Gulbarga (present-day Kalaburagi).
- The Bahmani rulers aimed to expand their territory into the fertile Raichur doab, which was controlled by Vijayanagar.

Conflict over the Raichur Doab:
- The Raichur doab was a strategically important region due to its fertile lands and proximity to both the Krishna and Tungabhadra rivers.
- Both the Vijayanagar and Bahmani kingdoms sought to control this region to secure their agricultural resources and increase their revenue.
- The control of the Raichur doab became a major bone of contention between the two kingdoms, leading to frequent conflicts and battles.
- The region changed hands multiple times between the Vijayanagar and Bahmani kingdoms, depending on the military successes of the respective powers.

Conclusion:
The Raichur doab, located between the Krishna and Tungabhadra rivers, constituted the permanent bone of contention between the kingdoms of Vijayanagar and Bahmani. Both kingdoms sought to control this fertile region to secure agricultural resources and increase their revenue. The control of the Raichur doab was a significant factor in the conflicts between the Vijayanagar and Bahmani kingdoms during the medieval period.