The British colonial administration became more repressive in Kerala after 1857 due to fears of:

Further revolts
French invasion
Spread of communism
Mysorean expansion

The correct answer is: A) Further revolts.

The British colonial administration became more repressive in Kerala after 1857 due to fears of further revolts. The Indian Rebellion of 1857, also known as the Sepoy Mutiny, was a major uprising against British rule in India. The rebellion began in Meerut, Uttar Pradesh, on 10 May 1857, and spread to other parts of India. The rebellion was eventually suppressed by the British, but it had a profound impact on British rule in India.

The British were concerned that the rebellion would spread to other parts of India, including Kerala. They were also concerned that the rebellion would be inspired by the spread of communism in Europe. The British colonial administration therefore became more repressive in Kerala after 1857 in an attempt to prevent further revolts.

The other options are incorrect. Option B, French invasion, is incorrect because the French were not a major threat to British rule in India after 1857. Option C, spread of communism, is incorrect because communism was not a major threat to British rule in India until the early 20th century. Option D, Mysorean expansion, is incorrect because the Mysore kingdom was not a major threat to British rule in Kerala after 1857.