The correct answer is: B) Pulakeshin II.
Pulakeshin II was the Chalukya ruler who is credited with building the cave temples at Badami. He was the son of Kirtivarman I and the grandson of Mangalesha. He ruled from 610 to 642 CE.
The cave temples at Badami are a group of Hindu and Jain temples located in the Badami district of Karnataka, India. The temples were built during the reign of the Chalukya dynasty. The most famous of the temples is the Virupaksha Temple, which is dedicated to the Hindu god Shiva.
The cave temples at Badami are a UNESCO World Heritage Site. They are considered to be one of the finest examples of early Chalukya architecture.
The other options are incorrect because:
- Mangalesha was the Chalukya ruler who ruled before Pulakeshin II. He ruled from 598 to 609 CE.
- Kirtivarman I was the Chalukya ruler who ruled before Mangalesha. He ruled from 566 to 598 CE.
- Vinayaditya was the Chalukya ruler who ruled after Pulakeshin II. He ruled from 642 to 681 CE.