Why blue colour of copper sulphate solution gets discharged when zinc rod is dipped in it?
(Given E°(Cu²⁺, Cu) = 0.34 V and E°(Zn, Zn²⁺) = 0.76 V)

Since E°(Zn, Zn²⁺) = −E°(Zn²⁺,Zn)=−0.76 V is lower than E°(Cu²⁺, Cu), therefore Zn will lose electrons and copper will accept them.
In other words, the following reaction will occur:

Zn + Cu²⁺ ⟶ Zn²⁺ + Cu

Since blue Cu²⁺ ions are consumed and colour less Zn²⁺ ions are produced during the above reaction, therefore the colour of CuSO₄ solution gets discharged when zinc rod is dipped in it.