X and Y are large, parallel conducting plates kept close to each other. Each face has an area A. X is given a charge Q. Y is without any charge, points A, B and C are as shown in figure.

If a large conducting plate is given a charge +Q, it is distributed equally on both surfaces. Charge density $\mathrm{\sigma }=\frac{\mathrm{Q}}{2\mathrm{A}}$. So the electric field at both points A and B due to the plate X is

$E_A=E_B=\frac{\sigma }{{\in }_0}=\frac{Q}{2A{\in }_0}$

If another uncharged plate is placed in front of charged sheet an equal and opposite charge  $-\frac{\mathrm{Q}}{2}$  is induced on inner surface and  $+\frac{\mathrm{Q}}{2}$ on outer surface. So  
${\mathrm{E}}_{\mathrm{C}}=\frac{\mathrm{Q}}{2\mathrm{A}{\in }_0}\mathrm{i}.\mathrm{e}$
${\mathrm{E}}_{\mathrm{A}}={\mathrm{E}}_{\mathrm{B}}={\mathrm{E}}_{\mathrm{C}}=\frac{\mathrm{Q}}{2\mathrm{A}{\in }_0}$
The directions of ${\mathrm{E}}_{\mathrm{A}},{\mathrm{E}}_{\mathrm{B}},{\mathrm{E}}_{\mathrm{C}}$ are shown in the figure.

Option (A) is correct.
Option (B) is wrong.
Option (C) is correct.
Option (D) is correct.