Which of the following reactions are disproportionation reaction?(a) $2{\text{Cu}}^{+}\to {\text{Cu}}^{2+}+{\text{Cu}}^0$ (b) $3{\text{MnO}}_4^{2-}+4{\text{H}}^{+}\to 2{\text{MnO}}_4^{-}+{\text{MnO}}_2+2{\text{H}}_2\text{O}$ (c) $2{\text{KMnO}}_4\stackrel{\Delta }{\to }{\text{K}}_2{\text{MnO}}_4+{\text{MnO}}_2+{\text{O}}_2$ (d) $2{\text{MnO}}_4^{-}+3{\text{Mn}}^{2+}+2{\text{H}}_2\text{O}\to 5{\text{MnO}}_2+4{\text{H}}^{+}$ Select the correct option from the following:

A disproportionation reaction is one where the same element in a single oxidation state is simultaneously oxidized and reduced.(a) ${\text{Cu}}^{+}$ ($+1$) goes to ${\text{Cu}}^{2+}$ ($+2$, oxidation) and ${\text{Cu}}^0$ ($0$, reduction). Yes.(b) $\text{Mn}$ in ${\text{MnO}}_4^{2-}$ ($+6$) goes to $+7$ in ${\text{MnO}}_4^{-}$ (oxidation) and $+4$ in ${\text{MnO}}_2$ (reduction). Yes.(c) This is thermal decomposition. $\text{Mn}$ ($+7$) goes to $+6$ and $+4$ (reduction only). Not disproportionation.(d) Comproportionation: $+7$ and $+2$ both go to $+4$. Opposite of disproportionation.