A parallel plate capacitor is charged by connecting it to a battery. Which of the following will remain constant if the distance between the plates of the capacitor is increased in this situation?

On increasing the separation between the plates the capacitance of the capacitor will be changed. 

As the battery remains connected with the capacitor, the potential difference remain constant, So the electric field will be changed(as separation is changed$E=\frac{V}{d}$)

And the energy stored in the capacitor is also changed.