You need Captivate.
Thanks but Captivate can't export as PDF.
Captivate won't work if it must be in the PDF. Technically, it could work if the computers have the Flash player installed and you export a SWF file, but Flash is not installed on many computers today.
For a simple option, use checkboxes that have the same name but different values; these will work like radio buttons but allow for deselection. However, radio buttons should work too. For example, all answers for question one are named Q1; the values are 10 for the correct answer and 0, 0.0, 0.00, for the wrong answers. (The extra zeros are treated as unique answers in Acrobat, otherwise, they would all turn on at the same time.) The Score, a read-only field would be a calculation of the checkboxes.
Here is a sample ID file with the PDF: https://shared-assets.adobe.com/link/9fc9863b-435d-4d49-7bfb-a2e9d152c22b
Thanks for the sample! I also need the PDF to lock itself once user clicks on the button "Start Grading" so the user cannot change the answers and a "Submit" button to send the results (+ a form with user information prior to taking the quiz) via email. Guess I will figure that out...
You could have the user digitally sign the "quiz", which can lock all the fields. Then the Submit button will send the form data (answers).