David Hirst’s answer is great. I can perhaps add a chemistry-related question that I was asked during one of my interviews.
“I have this substance,” he said, placing a small phial of white powder on the desk in front of me, “and I want to know what it is. What tests can I perform on it?”
I’ll give my best recollection of my answer below, but maybe have a think about it before scrolling down…
Me: “You could burn some of it and see what colour the flame is.”
Him: “Do you know what that is called?”
“Measuring the emission spectrum”
“Ok. Anything else?”
“Perform X-ray diffraction on it.”
“What does that do?”
(Slight hesitation, as I didn’t know in detail) “It tells you where the different atoms are in space with respect to each other.”
“What else?”
“Put it in a mass spectrometer.”
“How does that work?”
Bingo. I’d recently learnt about mass specs in A-level physics. Cue a hand-drawn diagram and descriptions of the ionisation chamber, the velocity selector, the detector, and which regions have electric and/or magnetic fields in them.
I’ll freely admit I got a bit lucky there!
One of the other questions I was given in that interview was “what do you think is the difference between a good Cambridge student and a great one?” It’s important to remember that not all the questions (= opportunities to impress) will be technical.
Good luck!