You get nothing from it so don't bother
You do get an Complimentary Archives Voucher - a piece of paper that you can trade it for some unique Mentats. To trade it, use a nearby terminal where you answered the quiz. and if you fail a question, don't worry - you can do it all over again. When you completed the quiz, you cannot get another Voucher. the only ones remaninig are on the 1st floor in a safe.