Two point charges (Q each) are placed at (0, y) and(0, -y). A point charge q of the same polarity can move along the x-axis. Then

Net force on qFnet =2Fcos⁡θ=24πε0Qqx2+y2xx2+y2=Qq2πε0xx2+y23/2  To maximize Fnet dFnet ′dx=0 or x=±y2.Hence (1) is correct.At origin x=0,Fnet =0. Hence (2) is correct. Since net force is away from origin, particle will not perform oscillatory motion.Hence (3) is incorrect and (4) is correct.