What should be value of  E for which galvanometer shows no deflection:

If reading of  G is Zero, then current through  20 Ω is zero. So voltage access  20 Ω is zero.Current in left circuit i1=205+10+5=1A current through the right circuit   i2=effective emfeffective resistance=10-E20Let say point A is at 0V. Then VD=0V , VB=10V , VC=10VUsing KVL,VC-5i2-E=0⇒10−510−E20-E=0∴E=10V