Why does 3-hydroxy-butan-2-one give positive Tollens' test? Why does 3-hydroxy-butan-2-one give a positive Tollens' test despite the absence of an aldehyde group? What is the mechanism?
From the Wikipedia entry on Tollens 1 


  Tollens' reagent is a chemical reagent used to determine the presence of an aldehyde, aromatic aldehyde and alpha-hydroxy ketone functional groups


The substrate you have drawn is an alpha-hydroxy ketone.