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 are the fields inside the cavity A and cavity B respectively? Where r_A and r_B are the unit vector from center of cavities respectively. 

q₁/4πε_or_A²   r_{A   ,}   q₂/4πε_or_B²  r_B 

since charges are enclosed inside the cavities, so use gauss law.