Among the following compounds, how many are reducing sugars, that is, give a positive Tollens' test: sucrose, maltose, lactose, trehalose, methyl…

A sugar reduces Tollens' reagent only if it has a free hemiacetal (anomeric) carbon that can open to an aldehyde, or an $\alpha$-hydroxy ketone that tautomerises to one. Maltose ($\alpha$-1,4-linked) and lactose ($\beta$-1,4-linked) each retain one free anomeric carbon, so both are reducing. D-Glucose is an aldose and reduces. D-Fructose, although a ketose, has the $\alpha$-hydroxy ketone unit and in basic medium isomerises to glucose and mannose through an enediol, so it is also reducing. Sucrose (the glycosidic bond joins the anomeric carbons of glucose and fructose) and trehalose (an $\alpha,\alpha$-1,1 linked disaccharide) have no free anomeric carbon; methyl $\alpha$-D-glucopyranoside is an acetal; D-sorbitol is a polyol with no carbonyl group. Hence four are reducing: maltose, lactose, D-fructose and D-glucose.