For the first time, arch-rivals India and Pakistan is to take part in
Right Answer is: B
The original phrase is incorrect as there are at least two nations involved and thus “are” would be used.
Option A is incorrect as taken is the past participle form of take and the statement seems to imply context of an occurrence going to happen in future.
Option C is incorrect as parted here implies to be separated from something/someone.
Option B is correct in terms of grammar and context.
Hence, option B is the correct answer.