For the reaction of A + 2B-  ---- A2+ + 2B Kc is found to be 10^12. The E0 cell is:
1. 0.708 V
2. 0.1777 V
3. 0.088 V
4. 0.354 V

Dear Student, 
From the relation between free energy and electrode potential;
​​G = -nFEcell
we know that at the equilibrium change in free energy is zero (ΔG) . hence Ecell becomes zero. 
From Nernst equation,
Ecell = E0 -0.0592nlogQ
Where Q is the reaction quotient.
As Ecell is zero we have, 
E0 = 0.0592nlogKc
Here we have replaced the Q by Kc as the reaction is in equilibrium. 
E0 = 0.05922log(1012) = 0.355 0.340 V

Regards​

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