The correct answers are Most of the students passed the exam. and Most students in this class passed the exam.

When using quantifiers like "most", "all", or "some", you can use them directly before a noun for a general statement (e.g., Most students). If you are talking about a specific group, you must use "of the" (e.g., Most of the students). You cannot mix the two rules by saying "Most of students" or "Most the students".