Tollen's reagent is a mild oxidizing agent that gives a positive test (silver mirror) with aldehydes and hydroxy ketones.
In cyclic structures, hemiacetals are in equilibrium with their open-chain hydroxy-aldehyde forms in aqueous solution, whereas acetals and ethers are stable and do not open up.
Compound A is a cyclic acetal (specifically a methyl glycoside type structure). It is stable and does not show Tollen's test.
Compound B is a cyclic ether with a methoxy group at a non-anomeric position. It is stable.
Compound C is a cyclic hemiacetal. The carbon attached to both the ring oxygen and the -OH group is the hemiacetal carbon. In solution, it exists in equilibrium with its open-chain form which contains an aldehyde group: . Therefore, it gives a positive Tollen's test.
Compound D is a cyclic ether with an alcohol group at a non-anomeric position. It does not have a hemiacetal linkage and will not give a positive Tollen's test.
Thus, the correct compound is C.