What is JotForm?
JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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We believe that if one user has a question, there could be more users who may have the same question. This is why many of our support forum threads are public and available to be searched and viewed. If you’d like help immediately, feel free to search for a similar question, or submit your question or concern.
I'm not sure if this will work as you need, as far as I know you can not create your "database" of questions and answers and only use them on different forms.
However, we have an app that will help you to create a test/quiz form, here is the link to the app: http://apps.jotform.com/app/quiz_form.
Here is a guide that will help you to turn your form into a quiz: http://www.jotform.com/help/289-Turn-your-form-into-a-Quiz-or-Exam-.
Hope this will help you.