Explanation:

Correct Answer is (c).The bold part in the sentence is not correct since there is problem with the use of the preposition ‘of’ in the sentence. If both is followed by a noun, there is no requirement to add the preposition ‘of’ with that though in case of a pronoun, this preposition is necessary. In this case, both is followed by a noun and that is why, both of the countries is not the correct phrase but both the countries should have been used.
The correct sentence would have been:
India has signed an agreement with South Korea in the area of nuclear power development and under this agreement the nuclear scientists from both the countries will work together to develop sustainable nuclear solutions for the world.This makes option C the correct choice among the given options.