A) Internal energy can remain constant, say for a gas if its temperature doesn't changes as ΔU=mCvΔT = 0 if ΔT is zero in the process
B) Internal energy and entropy are definitely state functions as they depend only on the final and initial states
C) It can be zero if process is fully reversible
D) From the first law, ΔW=−ΔU for an adiabatic process so work may be non-zero if ΔU is non zero