The ideas of traditional Chinese medicine, which integrates mental activity with body postures and respiration, provide the theoretical basis of an exercise; this exercise, with
many possible variations on a few basic standing postures, are known as "standing."
many possible variations on a few basic standing postures, are
many possible variations along with a few basic standing postures, are
many possible variations on a few basic standing postures, is
a few basic standing postures varied, are
the possible variations on their basic standing postures, is
Since the verb of the second independent clause, are, is underlined, you want to see if the subject and verb agree. Are is plural. The second independent clause has a singular subject, this exercise, which must take a singular verb, is, rather than the plural verb shown in the original sentence. Eliminate Choice A.
Since you have found an error in the original sentence, work through the answer choices, starting with Choice B, to see if any other answer choices contain the same error. Any answer choices that use plural verbs are wrong because plural verbs do not match the singular subject, this exercise. You can quickly eliminate Choices B and D because are is plural.
Now consider the remaining answers. In Choice E, the plural pronoun their does not unambiguously refer to any noun. So you can eliminate Choice E.
The correct answer is Choice C