If your users are going to be able to answer the questions quickly (Which of the following is an Impressionist painter? da Vinci, Rembrandt, Monet, Picasso) and they are going to quickly go to another problem then they will get duplicate questions very quickly. If they are using this trivia game in order to help learn a school subject they would have a different response than if they are doing it simply as a game.

The obvious answer is to test your user base. If the answer is that they would mind you have two solutions to the problem. Implement some "mechanism" to prevent this from happening or quickly ramp up the number of questions.

If your users are going to be able to answer the questions quickly, example: Which of the following is an Impressionist painter? (da Vinci, Rembrandt, Monet, Picasso) and they are going to quickly go to another problem then they will get duplicate questions very quickly. If they are using this trivia game in order to help learn a school subject they would have a more positive response than if they are doing it simply as a game.

The obvious answer is to test your user base. If the answer is that they would mind having questions repeated too quickly then you have two solutions to the problem. One,implement some "mechanism" to prevent this from happening or two, quickly ramp up the number of questions.