A hollow conductor carries a net charge of ++3QQ. A small charge of −−2QQ is placed inside the cavity in such a way that it is isolated from the conductor. How much charge is on the outer surface of the conductor?

The value is  

Explanation:

From the question we are told that

   The net charge is

     The  charge place on the  inside of the cavity is  

Since we are told from the question that small charge placed inside the cavity is isolated from the conductor

  Then it implies that the electric flux is  Zero

Which mean that the charge place within the conductor +  the charge  on the inner region of the conductor  =  0  

i.e

=>  

=>  

Now the net charge on the conductor is mathematically represented as

Here   is the charge on the outer surface

So

=>