Which is the correct order of decreasing acidity of the most acidic C-H hydrogens in pentane-2,4-dione (I), ethyl 3-oxobutanoate (II), diethyl propanedioate (III) and propanone (IV)?

The $\mathrm{CH}{}_2$ between two carbonyls gives an enolate stabilised by two $\mathrm{C}=\mathrm{O}$ groups. A ketone carbonyl accepts charge better than an ester carbonyl, because the ester oxygen lone pair competes by donation. So $p{K}_a$: pentane-2,4-dione ($\approx 9$) < ethyl 3-oxobutanoate ($\approx 11$) < diethyl propanedioate ($\approx 13$) < propanone ($\approx 19$). The acidity order is the reverse.