Is it possible to randomly select questions in a quiz?

Yes, it is possible.

When you add questions to a quiz you can choose to randomly select them from a category. Here’s how to do it:

After you add a quiz to your course, select Edit quiz from settings

 

Then select  add-> a random question from the menu on the right

In a new window you can select the category to randomly pick questions from and the number of random questions to show during the quiz.