There is no b7 th, just the root-3rd-5th (C-E-G) plus the 9th (D) added on top. On an instrument such as the guitar where ... to the triad (E-A-C#) that forms the A major chord at the 2nd fret ...

You’ll notice each major 7 chord has its own ‘EQ’ due to the different strings used. I’ve highlighted A for particular attention here because it’s such a nice key on the guitar ...