During alkaline KMnO4 oxidation brown precipitates of MnO2 are formed. Out of the alcohols listed only (CH3)3C−CH2OH is 1∘ alcohol and hence undergoes oxidation easily.
All the remaining alcohols are 3∘ and hence, do not under go oxidation easily. 2KMnO4+H2O→2MnO2+2KOH+3[O]