Here's what I found from UNC's Graduate Handbook:
There are five qualifying exams:
Algebra: Math 676 and 677
Analysis: Math 653 and 656
Geometry-Topology: Math 680 and 681
Methods of Applied Mathematics: Math 668 and 669
Scientific Computation: Math 661 and 662
Looking through previous courses, it's safe to say the Algebra Qual follows Dummit and Foote, the Analysis Qual follows Ahlfors and Baby Rudin, and the rest follow their own texts.
Most schools use Dummit and Foote for their Algebra Qual, the top schools use Lang, and for some reason, my school uses Aluffi, Serre's Rep Thy, and A-M. There was a question on derived functors and another on integral closures on my Algebra Qual.