The mural paintings inside the Jain caves at Badami date back to this period:

The correct answer is: A) 6th century.

The Jain caves at Badami are a group of Hindu and Jain cave temples located in Badami, Karnataka, India. The caves were built by the Chalukya dynasty between the 6th and 8th centuries CE. The caves are known for their intricate sculptures and paintings.

The mural paintings inside the Jain caves at Badami are some of the finest examples of early Indian painting. The paintings depict scenes from Hindu and Jain mythology, as well as scenes of everyday life. The paintings are executed in a style that is both realistic and stylized.

The paintings inside the Jain caves at Badami are an important part of the history of Indian art. They provide a glimpse into the religious and cultural life of India during the 6th and 7th centuries CE.

Here is a brief explanation of each option:

• Option A: The 6th century is the correct answer. The Jain caves at Badami were built by the Chalukya dynasty between the 6th and 8th centuries CE.
• Option B: The 10th century is incorrect. The Jain caves at Badami were built by the Chalukya dynasty between the 6th and 8th centuries CE.
• Option C: The 15th century is incorrect. The Jain caves at Badami were built by the Chalukya dynasty between the 6th and 8th centuries CE.
• Option D: The 18th century is incorrect. The Jain caves at Badami were built by the Chalukya dynasty between the 6th and 8th centuries CE.