In the following circuit the equivalent capacitance between points $A$ and $B$ is
(capacitance of each capacitor is $2\mu \mathrm{F}$)

Equivalent capacitance between $A$ and $B$ is

A parallel plate air capacitor has capacitance $\mathrm{C}$ Now half of the space is filled with a dielectric material with dielectric constant $\mathrm{K}=5$ as shown in figure. The new capacitance is

Figure shows a solid conducting sphere of radius $1 \mathrm{m},$ enclosed by a metallic shell of radius $3 \mathrm{m}$ such that their centres coincide. If outer shell is given a charge of $6 \mathrm{\mu C}$ and inner sphere is earthed, find magnitude charge on the surface of inner shell