What note is played at the 1st fret of the 2nd string?

The note played at the 1st fret of the 2nd string, which is the B string on a standard-tuned guitar, is indeed C.

To understand this, it's helpful to remember how the musical alphabet works. The notes follow the sequence A, B, C, D, E, F, G, and then repeat. The 2nd string of the guitar is tuned to B in standard tuning. When you press down on the 1st fret of that string, you're raising the pitch of the open B note by a half step.

This half step increase takes you from B, the open note, to C, the note found at the 1st fret. This half-step concept is crucial for identifying notes on the fretboard, as each fret corresponds to a half-step increase in pitch. Therefore, at the 1st fret of the 2nd string, you're correctly identifying the note as C.