Explanation:

- Option 1: Vigraharaja III

- He was an earlier Chahamana king who ruled before the famous battles with Muhammad Ghori.

- His reign is noted for providing a foundation for future military engagements.

- Option 2: Ajayaraja II

- Also an earlier Chahamana ruler, primarily recognized for establishing Ajmer as a significant city.

- Did not engage in battle with Muhammad Ghori.

- Option 3: Prithviraja III

- Known as Prithviraj Chauhan.

- Famously defeated Sultan Muhammad Ghori in the First Battle of Tarain in 1191.

- This victory is celebrated in Indian history as a significant resistance against foreign invasions.

- Option 4: Durlabharaja III

- Not directly associated with battles against Muhammad Ghori.

- His period was earlier and not marked by significant conflicts against Muslim rulers.