Can I reject a faulty used car bought from a dealer within 30 days?

Potentially yes, if it fails the legal standards of satisfactory quality, fitness for purpose or description.

The short-term right to reject is not an unconditional change-of-mind period. State the fault and that you are exercising your rights in writing, and preserve evidence. The dealer can dispute whether the defect was inherent; an independent report may help establish the facts.