right and correct are very much the same, and almost completely interchangeable. The difference is that right is more confirming that it's positive (it's good), while correct is confirming that it is not negative (no error, see Jane's comment). So, a very small nuance.

(btw, correct and right also share the same original stem from Latin (regere --> correctus, rectus))

For true, see Jane's comment, although 1+1=2 is also true.