The correct answer is: d) Became a state within India.
The Namgyal dynasty was a Tibetan Buddhist dynasty that ruled the kingdom of Sikkim from 1642 to 1975. The dynasty came to an end in 1975 when Sikkim became the 22nd state of India.
Option a) is incorrect because Sikkim was never conquered by Nepal. Sikkim was a vassal state of Nepal from 1793 to 1814, but it was never formally annexed by Nepal.
Option b) is incorrect because Sikkim became a part of British India in 1861. Sikkim was a princely state under British suzerainty until 1975.
Option c) is incorrect because Sikkim never merged with China. Sikkim was a buffer state between India and China, and it was never formally part of China.
I hope this helps!