I would like to give multiple choice tests with randomized questions and order of the answers that is unique for each test, to be printed and given on paper sheets. Is there a software that would do the randomization?
If you use LaTeX to prepare your documents, there are many packages that automatically randomize the order of choices in multiple-choice questions.
The package allows to write various type of exercises (multiple choiche questions with answers varying in random order, with closed or open answer, matching, problems, and so on). Questions of each group are randomly scrambled across the exam and variants of each exercise are chosen randomly from a file which contains them all and.
Pearson's TestGen is a crucial tool for my teaching for this reason and others. If you have an instructor account with Pearson, then the software download is free, and so are testbanks for almost all of their textbooks. The testbanks include premade questions of several different types, and of course you can write your own. It has well-constructed formatting for math equations.
Once you have a test made, it's a one-click process to scramble the order of any multiple-choice options. In addition to that, questions can have variable entities, so that another click randomly changes the visible numerical or text values within certain questions (works somewhat better for testbank multiple-choice items, or self-made short-answer items).
It also has an export feature which allows a test to be exported to HTML, Blackboard, or WebCT. For example: I find the test-creation in TestGen so much more elegant than Blackboard that all of my online quizzes are first drafted in TestGen, then exported to Blackboard. Plus my in-class tests use the random values/random ordering function each semester, with some manual edits to more conceptual short-answer/essay items.
During initial test construction you can insert a number of random questions from a premade testbank this way (from the TestGen Tutorial, p. 6):
And then later on you can scramble the order of any questions and.or answers with this menu button (tutorial p. 10):
In the past I also used Cengage's ExamView for one semester, but it didn't work nearly as well as TestGen.
I don't see why you couldn't use WeBWorK for this. It might be more powerful than you are looking for, if you don't want truly random questions (that is, random numbers for each problem), but it certainly can do this. Apparently they have just implemented new themes for hardcopy. Anyway, people may not know that WeBWorK problems are certainly available for physical exams/homework too (though those won't grade themselves!).
AutoMultiplechoice does that, including autocorrection using a scanner (there is a code telling the machine what was the order of the questions and answers).
It is compatible with LaTeX, but does not require it. It can be quite efficient, but I didn't have much experience with it up to now.
I would really like to find something that would work well in this regard. I have used both Tamarack TestGen and Wimba Diploma pretty extensively, but both have pros and cons.
TestGen has a horrible interface for typesetting mathematics, and very limited ability to refresh the numbers in questions (to create different versions). The quality of the typesetting is sometimes poor, so that it can be hard for students to read. For example, a complicated expression in an exponent won't be superscripted sufficiently so that it is clearly an exponent. The function which you use to change the numbers in a question, as I understand it, is basically ordered lists, so that if you had a question with three different values you wanted to change, you would support that question with three different "variables" that would pull values sequentially from the list linked to each variable. Different versions of the question would use the first value from each list, and then the second value from each list, and so on. So you are limited to the number of values entered into the list.
Diploma was last updated in 2012, so even though it is pretty user-friendly and the typesetting is good (it uses Equation Editor from MS Word, or MathType), and it has some power to generate many versions of a question, it looks like it won't be updated. Wimba, the parent company, was bought by Blackboard, and publishers seem to be deserting the software. I don't know how much longer it will be operating, which is unfortunate as I have spent many hours writing questions in Diploma banks for use in my work.
WeBWorK also seems to be slowly dying, and so far as I understand-- I used it about a decade ago-- has no ability to generate multiple versions of an exam with a key.
An editor from a major publisher described the considerable money being spent by said publisher to allow online delivery of assessments. This is driving everything right now. Is it too much to expect software that does both paper-based and online exams well?