The correct option is B claims
The context refers to a person asserting that he had answered most questions correctly, yet had gotten low marks. Here, "claims" in option B fits best as it means stating or asserting that something is the case, typically without providing evidence or proof. Thus, option B is correct.
"Contracts" in option A means becoming short and tight. This does not suit the context.
"Blames" in option C is incorrect as blame is put on other people whereas, he is asserting about his own work.
"Conceives" in option D means to create a mental representation of something. The context implies that the subject is communicating with others.
Thus, option B is correct.