Status of non expired B1 visa after getting J1 Visa stamping

[drdileepunni]

Hi,

I am planning to re-enter US after my J1 Visa expires to take my ABIM board exams. This is because my J1 grace period is only 30 days after expiration of the VISA and my exam is at a later date. I am planning to enter on a B1 visa which is still not expired (till 2021). Is there a chance of them rejecting my entry? Is a B1 visa still valid after the passport being stamped with a J1?

Thank you for the help
drd