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There are two possibilities depending on where A is.

If A is on one side of both P and Q, then net force can be zero, only if one charge is higher and another smaller and both are oppositely charged.  It will be possible when the charges A, P and Q are collinear.

Net force on A will be zero, if A is in between P & Q and they are both of the same polarity.  ie., both positive or both negative.  Here the to forces will be in opposite directions.  Assuming that A,  P, and Q are on the same straight line.  Here is it possible that on e charge is higher than the other.