Hm, that scenario question comment sounds a little familiar.

Some questions I've found are helpful with sorting are things like:
Do you prefer to be in the front lines, in the back supporting, or a little of both?
The victory fanfare cues! What's your victory pose like?
What's one trait you admire most in other people?
It turns out you have the ability and the chance to save the world from a catastrophe. Would you honestly do it?
Let's say you decide to save the world. What are your reasons, and would you gather a team to help you or do it alone?
Since you saved the world from doom, it's landed you in a position of power. (Congrats you're now King/Queen of the world!) What do you intend to do with this power?
Apparently someone really hates what you're doing and it seems they want you dead. They have the plans in place to see this through. What are you going to do about it?

And to do some specific copy pasta, I think this shows an interesting look at someones preferences and the like.

How do you feel about:
...using charm/confusion/distraction to your party's advantage?
...utilizing stealth to gain the upper hand?
...being able to call a non-human companion to your aid?
...inventing/creating things on the spot to help your teammates out?
...using music/creativity as your weapon?
...specializing in abilities that nullify attacks and lower enemy stats?
...copying others' abilities at the cost that they are not as a strong?
...letting Lady Luck be your guide in battle?
...sacrificing your own health to perform stronger attacks?
...making your primary duty to protect your allies, even risking being a human shield?

Now obviously that's a little extensive for our class system, but I think it'd be interesting to have some questions that are specifically about how the applicant views the class abilities/classes.