Depends on the school. My program requires you have an advisor before our version of quals. Our exam was also a research presentation followed by an oral exam w

Depends on the school. My program requires you have an advisor before our version of quals. Our exam was also a research presentation followed by an oral exam where you had the pleasure of doing often a painful amount of algebra on a blackboard. It was also the culture that, while your advisor could ask you questions, they rarely would unless they were helpful (maybe a softball confidence booster or simple version of another question to get you started down the right track) or leading questions for you to talk about something not in your talk. People were largely concerned about being failed by the other examiners, not their advisor at that stage. However, we were a small department and your acceptance was predicated on at least one faculty member wanting you to join their lab. Some people moved around within their first year, but the majority stayed with the first group they joined.