1. A hollow conductor carries a net charge of +3Q. A small charge of -2Q 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?

+Q

Explanation:

As no electric field can exist (in electrostatic condition) inside a conductor, if we apply Gauss 'Law to a spherical gaussian surface with a radius just a bit larger than the distance of the inner surface to the center (but less tah the distance of the outer surface), the net flux through this surface must be zero, due to E=0 at any point of the gaussian surface.

Therefore, as the net flux must  be proportional to the  charge enclosed  by the surface, it follows that Qenc = 0.

⇒ Qenc = Qc + Qin = -2Q + Qin = 0 ⇒ Qin = +2Q

So, if the net charge of  the conductor is + 3Q (which must remain the same due to the conservation of charge principle) and no charge can exist within the conductor (in electrostatic conditions), we have the following equation:

Qnet = Qin + Qou = +3Q ⇒ +2Q + Qou = +3Q

⇒ Qou = +Q