Two non-conducting spheres of radii $${R_1}$$ and $${R_2}$$ and carrying uniform volume charge densities $$ + \rho $$ and $$ - \rho ,$$ respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region

Six point charges are kept at the vertices of a regular hexagon of side $$L$$ and center $$O,$$ as shown in the figure. Given that $$K = {1 \over {4\pi {\varepsilon _0}}}{q \over {{L^2}}},$$ which of the following statement(s) is (are) correct ?

A cubical region of side $$a$$ has its center at the origin. It encloses three fixed point charges, $$-q$$ at $$\left( {0, - a/4,0} \right), + 3q$$ at $$\left( {0,0,0} \right)$$ and $$-q$$ at $$\left( {0, + a/4,0} \right).$$ Choose the correct option(s)

A spherical metal shell A of radius $${R_A}$$ and a solid metal sphere $$B$$ of radius $${R_B}\left( { < {R_A}} \right)$$ are kept far apart and each is given charge $$' + Q'.$$ Now they are connected by a thin metal wire. Then