Why don't you move abroad?

Forgive me if I'm being elitist here, but this seems like a strange example of outrageous admission requirements. I would have thought knowing about radiocarbon dating (which I'm assuming this is a reference to) is common knowledge (I believe it's in the standard curriculum for grades 7-9 in my country), so it doesn't seem like a completely unreasonable test question. If this is an example that the author uses from his or her own experience, it seems stranger still.

>Every evening, my brother and I would sit in front of an oil lamp and study, mostly maths and science.

I think there's a big step from that knowledge to say that means I know the basics of nuclear physics. If anything, it's a better test for the basics of archaeological dating.

Or, as I learned recently, the 12C/13C/14C ratios are used to help determine the source for the increase in atmospheric CO2, since fossil fuels have essentially no 14C. (TIL it's the "Suess effect", https://en.wikipedia.org/wiki/Suess_effect ). So it can also be a test for how well one understands the evidence behind the causes for global warming (while also making carbon dating trickier - https://www.pnas.org/doi/10.1073/pnas.1504467112 ).

I also know that nuclear power plants split the uranium atom to generate power, as do atomic bombs. I also know that radioactive materials are used in smoke detectors and as power sources for some space probes, that bananas are radioactive, and that radon is a radioactive gas that can build up in houses and cause cancer.

That still doesn't mean I know the basics of nuclear physics, which starts with how the nucleus contains protons and neutrons, and is incredibly tiny compared to the nominal size of the atom.