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In Swiss federal institutes grad students are paid but it's free for undergrads.

I'm afraid it isn't free for undergrads, even outside the federal domain. Actually St Gallen is more expensive than ETH! https://www.unisg.ch/en/studium/informationsangebote/gebuehr...

Free for undergrads here meaning that they attend school for free (no tuition), or that they are not paid? Or both?

For undergrads, no tuition fees and they are not paid