[GTP]

I mean a final exam at the end of the program covering not just a single subject but potentially anything you studied during the program. But in practice it has to be more restricted, that's why they ask him what he prepared: it could be potentially anything, but to practical reasons they have to restrict it to a few subjects. Still more fields than what is covered by a single course. Or at least this is my interpretation.

[bmitc]

I knew what you meant, but as I said, these type of exams are not at the end of a PhD program. At Princeton, it appears that the general exam occurs after year one or two: https://www.math.princeton.edu/graduate/requirements