In order to insure my place in infamy, I created my own irrelevant questions. Well, not exactly a question, more of a process. I would show the applicant a PCB from the company product, and ask them to identify components that they've worked with in the past, and give a short description on what they do. Ostensively, this was to gauge experience. Most would recognize about 25% of the major RF components, which was about what I would expect. I then explained what the board did, what products it was used in, some of the parts they missed, and generally filled in the blanks.
I would then give the applicant a tour of the factory, production line, grab a cup of coffee, and return to my messy office where I would hand the applicant the exact same PCB, and ask the exact same question. The real test was whether they were paying attention and how much of my explanation they were able to recall. 50% recognition was typical. Exceptional engineers and techs, which unfortunately we couldn't afford to hire, would come very close to 100% recognition and recall.
Other companies use the interview for testing problem solving skills. <http://en.wikipedia.org/wiki/Microsoft_Interview> Now, that's what I call relevant questions. However, it's occasionally abused by asking the applicant to solve a real problem with a current product. I once interviewed at a company that did that to me. I was presented with a large schematic of the product, and asked to critique the design. After a few minutes of hasty back of the envelope calculations, I declared the product to be over-designed, a tolerance accumulation nightmare, and that there were several active stages that were superfluous. I offered specific recommendations on what should be changed. I then expect to be thanked for my brilliant insights. Instead, I was diplomatically thrown out the door. It seems that the manager that was conducting the interview had designed the product, and did not take kindly to criticism. So much for a relevant problem solving interview.