The correct option is C None of the above
Let the third charge −q is placed at a distance of x from the charge 2 q. Then potential energy of the system is
U=k[(2 q)(8 q)r−(2 q)(q)x−(8 q)(q)r−x]
U is minimum, where
2x+8r−x is maximum.
For y to be maximum dydx=0
But at x=r3,d2ydx2= positive
i.e., at x=r3, y is minimum or U is maximum. So, there can't be any point between them where potential energy is minimum.