Doubt from electrostatics

#1

please explain 76th question

#2

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#3

I have a small doubt about an extension to this question:

Where does the induced charge on the spherical shell reside ?

I know that excess charge always resides on the exterior of the conductor so induced charge should reside on the outer surface of shell. But if the excess charge resided on the outer surface then it would violate law of conservation of charge as initially charge on the shell was 0 and so there must be some charge induced even in the interior of the shell.

Can you help me out ?

#4

Yes the net charge induced at the surface of conductor is zero but it need not necessarily be zero everywhere in the surface .
Only sum of all the charges induced in the surface of conductor be zero.
In the above question the induced charges will have a non uniform distribution in the surface but the net charges induced is zero.