Is it permissible to be slow in answering in order to avoid fame, and what is the ruling on guessing in objective exam questions when the correct answer is not known, and does the sin fall upon the student or the department when the student's pictures are published in the press after he achieves first place?

You are advised to strive hard in the exam and achieve first place, for Allah loves perfection in work, and excellence in beneficial sciences is a strength that Muslims should acquire. The dissemination of the image should not be an obstacle to achieving prominence, for the forbidden act is minor compared to the benefit gained from the excellence of a committed Muslim in their studies. It is feared that this question might be a temptation from the self to hinder diligence. There is no harm in guessing the answers to questions whose correct answers you do not know.