The correct answer is C. against.
The English schemed to continue their rule in India by playing off one community against the other. This means that they would pit different groups of people against each other, so that they would be too busy fighting each other to unite against the English. This strategy was very effective, and it allowed the English to maintain their rule in India for many years.
The other options are not as accurate. Option A, before, does not make sense in the context of the question. Option B, upon, could be used to describe the way in which the English imposed their rule on India, but it does not accurately describe the way in which they maintained their rule. Option D, with, could be used to describe the way in which the English worked with some Indian groups to maintain their rule, but it does not accurately describe the way in which they played off one community against the other.