SQL: can many to many relationship have a PK in addition to the FKs from the other entities

Question

I'm having problem in inserting the values of an exam in the DB, and the reason is that every question that have been taking in the exam need to be unique which is not the case, we want the system to allow us to duplicate questions in the 60 question exam. what can I do to make this happened?

Exam (ExamID, Student.UID,  ExamFB, Evaluated, ExamLevel)
Primary key (ExamID)
Foreign Key (Student.UID)
Contains (ExamID, QID, X, Y, StdAnswer, CorrectAnswer, QuestionFB)
Primary key (ExamID, QID)
Question (QID, SecID, Supervisor.UID, QBody, LawID)
Primary key (QID)
Foreign key (SecID, Supervisor.UID) 

Answer 1

Add an IDENTITY Attribute with the FKs together will be your PK

Answer 2

Yes, a many to many junction table does not have to be unique, although in your scenario I imagine it should be, I don't see why you would have the same question more than once on an exam, however it is quite a common scenario, to pick a slightly different scenario, imagine a service history of a car, you might have a table of mechanics, and a table of cars, and a table to store each service:

Mechanics - MechanicID (PK) Name

Cars - CarID (PK), RegistrationNumber, Make, Model

It is possible that the same mechanic will service the same car more than once, so you can't make the primary key (CarID, MechanicID), so you would either need to just assign a surrogate primary key to the service table:

Services - ServiceID (PK), CarID (FK), MechanicID(FK), ServiceDate

Or add an additional column to your table that will make the composite key unique, e.g in the above make the key (CarID, MechanicID, ServiceDate).

In your case you could have an additional column QuestionNumber (1 - 60 in your case) that identifies where the question appears in your exam, then your PK would just be (ExamID, QuestionNumber), and keep the foreign key to QuestionID.

So your database diagram would look something like one of the below: