The correct answer is (C) has been studying.
"Since Sheenam has been studying diligently for months, she will clear the competitive exam."
The sentence uses "since" indicating an action that began in the past and continues to the present, requiring Present Perfect Continuous tense ("has been studying"). The subject "Sheenam" is third-person singular, so "has" is correct, not "have." Options (A) and (B) are grammatically incorrect in this context.