Neutral shell (with a charge inside) in an electric field 
A positive point charge $Q$ is kept eccentrically inside a neutral conducting shell. An external uniform field $E$ is applied. Then:
a) Force on $Q$ due to $E$ is zero
b) Net force on $Q$ is zero
c) Net force acting on $Q$ and conducting shell considered as a system is zero
d) Net force on the shell due to E is zero

My try:
Since the shell is neutral, thus net force on it by E must also be zero.
Also since Q is electrostatically shielded(by placing it inside a shell), thus net force on it must also be zero.
But the answer I'm getting(as you might have guessed) is wrong(that's why I've asked this question).
Please point out the flaw in my reasoning.
 A: You may start thinking in the following way,
Any neutral conductor placed in an electric field suffers induction and charge separation making it more of a dipole than a neutral conductor, this forces the conductor to interact with the field and move accordingly if unbound.
When we place something inside a conductor with cavity and switch on an external field 2 things happen, first is that the conductor with cavity suffers from induction as described above and then the resultant of both these fields (both external and that formed due to induced charges) is applicable all around. 
It just happens to be that the induction for a conductor and generally metals seem to take place so as to provide as much opposing field inside its bulk as that of the external electric field cancelling both out.
What this means is that even though the interaction of something inside a cavity of conductor with external field is not zero, the net electric field which decides whether it feels anything so as to move or anything is a combination of external field and induced field which is always 0 for conductor.
I hope this clears any doubts but you may ask in comments if you still are unable to solve your problem.
A: (a) Force on Q due to E is zero (true)
(b) Nett force on Q is zero (false)
(c) Nett force acting on Q and conducting shell as asystem is zero (false)
(d) nett force on shell due to E is zero (true)
