Miscellaneous logic puzzle from exam

[mangoezzz]

This is a question I stumbled on from an exam. Has anyone got an idea?

 

[EventHorizon]

I looked at that for a while.  Though it's not much, here's what I got...

Spoiler

8^2 = 64 = 6 *(10) +4

9^2 = 81 = 1*(100) -2*(10) +1

10^2 = 100 = 1*(100)

11^2 = 121 = 1*(100) + 2*(10) + 1

? = 12^2 = 144 = 1*(100) + 4*(10) + 4

So I'd guess D.  D also is connect diagonally like all the others.

But, I have no idea what the vertical position would mean, nor why 81 would be represented using a white token instead of simply going with an 8 and a 1.

I'm also not sure why the board/grid looks like it does, with that bar at the top.

 

[plasmid]

Spoiler

Is it from a music exam?

Those look sort of like patterns for fretting the strings of a guitar. But most of them aren't conventional chord shapes and the numbers don't make sense since most people don't have six fingers on their fretting hand.