A battery is of emf E is being charged from a charger such that positive terminal of the battery is connected to terminal A of charger and negative terminal of the battery is connected to terminal B of charger. The internal resistance of the battery is r. 

a) Potential difference across points A and B must be more than E. 

b) A must be at higher potential than B

c) In battery, current flows from positive terminal to the negative terminal 

d) No current flows through battery

A battery is of emf E is being charged from a charger and hence current inside the cell is from anode to cathode 

I = (V−E​)

V = E + Ir

Therefore, when a cell is being charged the potential difference across its terminals is greater than emf of a cell. Also in charging the positive terminal is connected to anode of the cell and negative terminal to cathode.

Here, positive terminal of the battery is connected to terminal A of charger and negative terminal of the battery is connected to terminal B of charger.

Hence, Potential difference across points A and B must be more than E, A must be at higher potential than B and In battery, current flows from positive terminal to the negative terminal