If they have supplied both the betas, use the adjusted beta. However, if they have supplied a beta by itself without any mention of adjusted/unadjusted, you shouldn’t be adjusting anything, especially in the equity section on the exam.
They could get evil by incorporating portfolio theory in the equity section, supplying an unadjusted beta, but asking us to use the adjusted beta for CAPM calculations. Even in that case, I’d think they would supply us with the “adjustment equation” (like 0.333 + 0.667x). So if the unadjusted beta is 1.5, adjusted beta for calculation would be 1.33.