Twelve identical cells, each of emf E and internal resistance r ,...

Total number of cells is $12$. One cell is connected with reversed polarity.

Net emf of the circuit is $E_{net} = 11E - E = 10E$.

Total internal resistance of the circuit is $R_{net} = 12r$.

Current in the closed loop is $I = \dfrac{E_{net}}{R_{net}} = \dfrac{10E}{12r} = \dfrac{5E}{6r}$.

The current flows in the direction of the $11$ correctly connected cells, meaning it enters the positive terminal of the reversed cell. Thus, the reversed cell is being charged.

The terminal potential difference across a cell being charged is given by $V = E + Ir$.

Substituting the value of $I$:

$V = E + \left(\dfrac{5E}{6r}\right)r = E + \dfrac{5E}{6} = \dfrac{11E}{6}$.

Answer: $\dfrac{11E}{6}$