Two point charges each of magnitude Q are placed at coordinates (0,y) and (0,-y)  A point charge  q of the same polarity can move along X-axis. Then:

For any position of (x,0)  other then origin the force is directed away from origin
$\mathrm{F}=\mathrm{a}\left(\frac{\mathrm{K}\left(2\mathrm{Q}\right)\mathrm{x}}{{({\mathrm{x}}^2+{\mathrm{y}}^2)}^{3/2}}\right)$
Thus for F to be maximum, we solve for $\mathrm{dF}/\mathrm{dx}=0$  which gives
$\mathrm{x}\pm \frac{\mathrm{y}}{\sqrt{2}}$
The charge is in equilibrium at the origin where net electric field due to the two charges is zero. However, the equilibrium is not stable since the force is repulsive along x direction and it will not be able to restore the charge at the origin. The charge therefore cannot perform oscillatory motion. Thus options (A), (B) and (D) are correct.