To solve this question, the user needs to know the subject-verb agreement rules in English grammar.
The subject in this sentence is "there", which is a dummy subject. The verb should agree with the complement of the sentence, which is "no doubt". "No doubt" is a singular noun phrase, so the correct verb to use is "is".
Option A is incorrect because it uses the plural verb "are", which does not agree with the singular noun "no doubt".
Option B is correct because it uses the singular verb "is", which agrees with the singular noun "no doubt".
Option C is incorrect because option B is the correct answer.
Option D is also incorrect because "both a and b" does not accurately describe the situation.