I'm assuming you are meaning class in an OO sense. So, if I were doing it, of course you would have a Game class. Since you are having Categories, there should be a Category class, and you can have a class that represents the question.
The Category class would have a collection of questions (I'm a Java programmer that hasn't done C++ in about 7 years so you'll have to translate class types for me). The Question class would have attributes of the question and answer (you could have an array of possible answers if you want to make it multiple choice, and you could get fancy with true/false answers too).
Sorry, I can't get a UML diagram to paste in this answer box! /forums/images/icons/smile.gif