Algebra
You can find some previous Algebra Qualification Exams Here: Previous Algebra Qualifying Exams
I have written up some solutions to a few of these Algebra Qualifying Exams below (Errata are appreciated!)
May 1989
September 2004
September 2008
Analysis
You can find some previous Analysis Qualification Exams Here: Previous Analysis Qualifying Exams
Galois Solutions
I have written up some solutions to A Course in Galois Theory by D.J.H. Garling below, any errata are appreciated.