They aren't among the "seven words you can't say on television." People were once conscious of a vulgar meaning of "nuts" (testicles). "Nuts" still has that meaning, but nobody thinks of it when they say or hear "are you nuts?" They are strong simply because of their meaning. "Are you dumb?" is insulting, but no worse than "are you stupid?" "Are you nuts?" is insulting, but no more so than "are you insane?" They definitely can cause hurt feelings if people think you are serious. They are the kind of things you say about someone else who's not in the room and can't hear them.

I would avoid using these at all. But if they must be used, use them with good friends you insult as a joke. Say it with a laugh. If not, it can be really insulting. Are you dumb is more if someone did something stupid that they didn't think through or they don't understand something you think should be easy to understand. Are you nuts? Would be more when someone does something dangerous or extreme and you're shocked. sometimes you can say it if you find it funny someone is doing something that extreme .

Excuse me, "are you dumb?" is what I meant to say -- It's pretty much the same as saying "you are dumb", which is why I confused it before haha

I agree with Jessica on the "are you nuts?" But saying "you are dumb" is juvenile, disrespectful, and immature. Don't use it if you want to learn proper etiquette.