The correct decreasing order of the acidic strength of `HClO, HClO_(2), HClO_(3),HClO_(4)` is

Explanation

The order of decreasing acidic strengths is :
`HClO_(4) gt HClO_(3) gt HClO_(2) gt HClO`
This is justified on the basis of the relative stabilities of anions formed after losing `H^(+)` ion. The order is :
`ClO_4^(-) gt ClO_3^(-) gt ClO_2^(-) gt ClO^(-)`
The ion `ClO_4^(-)` is maximum stable because negative charge dispersed by four electronegative oxygen atoms. At the same time `ClO^(-)` ion is least stable since it has only one oxygen to accommodate the negative charge. Thus, `HClO_(4)` has the maximum `H^(+)` ion losing tendency and is the strongest acid while `HClO` because of similar reason is the least acidic in nature. Also more is the oxidation number on the central chlorine atom more is the acidic strength. In `HClO_4`, chlorine has the highest oxidation number which is `+7` (most acidic) whereas in `HClO`, chlorine has least oxidation number which is `+1` (least acidic).