In-tray exercise usually assesses your prioritisation skills and whether you understand how the role of a Trainee works, whether you understand how long certain tasks should take, as well as whether you understand how you can use business services roles (i.e., Admin) to help you in your day-to-day.
I haven’t done an in-tray exercise recently, but I have done an e-tray exercise which had 3 options: Do, Delegate, and Defer.
Do = Urgent & Important tasks
Delegate = Things which are of importance, but do not necessarily have to be you doing it, i.e., book a meeting room for a big client meeting.
Defer = Things which are not client-facing / detrimental to your colleagues, e.g., responding to a summer party invite.
If it’s an e-tray, you’ll usually be given a set of emails, which you have to then place in each category after reading through them and understanding what they require.
If it’s an in-tray, I think that is usually physical documents, which you’ll either have to rank in order of priority, place in a category (similar to the above), or select choices on the best course of action. I’ve heard different structures, but at its core, just testing your prioritisation and understanding.