Answer:
to represent the interests of the crown
Explanation:
The British Viceroys are otherwise known as Governor Generals. They are the eyes and ears of the British empire. They serve the British crown and rule on its behalf.
Hence, in this case, the correct answer is "beginning in the 1800s, the British government appointed viceroys in India "to represent the interests of the crown."
For example Lord Canning, Lord Elgin, Lord Lawrence, etc.