The correct answer is: b) Late 1800s and early 1900s.
The Lushai Hills are a mountainous region in northeastern India, now part of the state of Mizoram. The area was inhabited by the Lushai people, who were a fiercely independent people. In the late 1800s, the British began to expand their rule into the Lushai Hills. The Lushai people resisted British rule, and there were a number of uprisings against the British. The most significant uprising was the Lushai Rebellion of 1895. The rebellion was led by Thangkhopao, a Lushai chief. The rebellion was ultimately unsuccessful, but it did lead to the British granting the Lushai people a degree of autonomy.
The other options are incorrect. Option a) is incorrect because the British did not begin to expand their rule into the Lushai Hills until the late 1800s. Option c) is incorrect because the most significant uprising against British rule in the Lushai Hills occurred in 1895. Option d) is incorrect because the Lushai people were not granted full independence until 1947.