Two spherical cavities (A and B) of radii x and y are hollowed out from the interior of a conducting sphere of radius R. Charges q₁ and q₂ are placed at centre of cavities A and B. The situation is depicted in the figure given:

What is the electric field outside the conductor at distance r from the center of large sphere? Take r as unit vector from centre of large sphere. 

(q₁ + q₂)/4πε_or²   r

Electric field outside will be due to the surface charges on the outer surface.