A solid metallic sphere of radius a is surrounded by a conducting spherical shell of radius b $\;(b >a)\;$ . The solid sphere is given a charge Q . Potential at the surface of the solid sphere is $\;V_{a}\;$ and at the surface of spherical shell is $\;V_{b}\;$. If we put -4Q charge on the shell the potential differance between the sphere and shell becomes $\;\bigtriangleup V\;.$ Now we earthed the outer shell and the charge on the ouer shell is $\;q_{1}\;$.Now we removed the earthing connection from the shell and earthed the inner solid sphere. Charge on solid sphere becomes $\;q_{2}\;$. Answer the following question based on the passage.Now if we connected the shell and solid sphere after removing earthing from the solid sphere charge on outer surface of shell becomes.

Question

$(a)\;\large\frac{Q(a+b)}{(a-b)}\qquad(b)\;\large\frac{Qa^2}{b}\qquad(c)\;\large\frac{Q(a-b)}{b}\qquad(d)\;-\large\frac{Qb}{a}$