Without the first note, you can't tell if it's B minor or D major.
Dmaj is the relative major of Bmin, same-same, so that's not it... (also, a piece in Bmin could start with a D, or any note for that matter, so knowing the first note wouldn't clarify this anyways)
(I know it's like those are sharps or something...)
correct! Bmin/Dmaj has two sharps, F# and C# - but in the image above, the second sharp is on B not C.