Answer: B, D
Mutarotation needs a free hemiacetal carbon (ring O and OH on the same carbon) so that the ring can open and close to give either anomer. Structure B (beta-D-fructofuranose, with a hemiketal C-2) and D (alpha-D-galactopyranose) have this. A is a methyl glycoside (acetal) and C is glucitol, with no carbonyl or hemiacetal, so neither mutarotates.