The correct option is
B a lot of students
The given sentence is missing a subject and thus, the answer has to introduce a subject. Further, the word 'are' indicates that the subject is plural. Thus, the answer has to be plural.
Option A is incorrect. In 'many student', 'many' is an adjective used for plural subjects but 'student' is singular. Thus, the phrase itself is grammatically incorrect.
Option B is incorrect. 'much student' also has a singular subject and not a plural one. Further, 'much' is an adjective normally used for things and not people. Thus, it is incorrect.
Option C is correct. In 'a lot of students', 'a lot of' is an adjective of quantity used for plural subjects and 'students' is a plural subject. Thus, it fits in the blank and is the correct answer.
Option D is incorrect. In 'a lot of student', 'a lot of' fits in the sentence but, 'student' is a singular subject and not a plural one as required. Thus, it is incorrect.