The correct answer is: C. 1843 AD.
Kaithal Principality was annexed by the British East India Company in 1843 AD. The annexation was part of the British expansion into the Indian subcontinent. The British East India Company was a private company that was granted a monopoly on trade with India by the British Crown. The company began to expand its territory in India in the early 18th century. The annexation of Kaithal Principality was a significant event in the history of British India. It marked the beginning of the end of the independent princely states in India.
The other options are incorrect. Option A is incorrect because Kaithal Principality was not annexed by the British East India Company in 1818 AD. Option B is incorrect because Kaithal Principality was not annexed by the British East India Company in 1824 AD. Option D is incorrect because Kaithal Principality was not annexed by the British East India Company in 1850 AD.