Which of the following reactions are disproportionation reactions?
$(a)$ $2 Cu^{+} \rightarrow Cu^{2+} + Cu^{0}$
$(b)$ $3 MnO_{4}^{2-} + 4 H^{+} \rightarrow 2 MnO_{4}^{-} + MnO_{2} + 2 H_{2}O$
$(c)$ $2 KMnO_{4} \xrightarrow{\Delta} K_{2}MnO_{4} + MnO_{2} + O_{2}$
$(d)$ $2 MnO_{4}^{-} + 3 Mn^{2+} + 2 H_{2}O \rightarrow 5 MnO_{2} + 4 H^{+}$
Select the correct option from the following:

• A
  $(a)$ and $(b)$ only
• B
  $(a), (b)$ and $(c)$
• C
  $(a), (c)$ and $(d)$
• D
  $(a)$ and $(d)$ only