Introduction:
Jainism is an ancient Indian religion that emerged around the same time as Buddhism. It emphasizes non-violence (ahimsa) and the pursuit of spiritual purity. Jainism had a significant presence in the southern region of Mysore, but it was eventually ousted from the area. The correct answer to the question is option B, Sankaracharya.

Sankaracharya:
Sankaracharya, also known as Adi Shankaracharya, was a philosopher and theologian who lived in the 8th century CE. He was a proponent of Advaita Vedanta, a school of Hindu philosophy that emphasizes the non-dual nature of reality. Sankaracharya is credited with the revival and reorganization of Hinduism and the establishment of monastic orders (mathas) in different parts of India.

Conflict with Jainism:
During his time, Sankaracharya engaged in debates and discussions with various religious and philosophical groups, including Buddhists and Jains. His debates with Jain scholars were particularly significant in the context of Mysore.

Philosophical Differences:
Jainism and Advaita Vedanta have fundamental philosophical differences. Jainism advocates for the existence of eternal and individual souls (jivas) that undergo cycles of birth and death until attaining liberation (moksha). In contrast, Advaita Vedanta posits the ultimate oneness of the individual self (atman) with the universal consciousness (Brahman), denying the existence of separate individual souls.

Impact of Sankaracharya:
Sankaracharya's debates and teachings had a profound influence on the religious landscape of Mysore. His promotion of Advaita Vedanta and the establishment of monastic orders attracted many followers and disciples. This led to a decline in the popularity and influence of Jainism in the region.

Conversion of Followers:
As Sankaracharya gained more followers and his teachings spread, many individuals who were previously followers of Jainism converted to Advaita Vedanta and Hinduism. This gradual shift in religious allegiance contributed to the ousting of Jainism from Mysore.

Conclusion:
In conclusion, Sankaracharya's promotion of Advaita Vedanta and his debates with Jain scholars played a significant role in ousting Jainism from Mysore. His teachings attracted followers and led to a decline in the popularity and influence of Jainism in the region.