Three charges $+Q, q, +Q$ are placed respectively, at distance, $0, d/2$and $d$from the origin, on the $x-$axis. If the net force experienced by $+Q$, placed at $x=0$, is zero, then value of $q$ is

By Coulombs law, the electrostatic force between the charges Q at x=0 , Q at x=d  is $\frac{K.Q^2}{d^2}$

the electrostatic force between the charges Q at x=0, q at x=d/2 is $\frac{K.Qq}{{\left(d/2\right)}^2}$

As the net force is zero 

$\frac{KQQ}{d^2}+\frac{KQq}{{\left(d/2\right)}^2}=0$

$Q+4q=0$  $\Rightarrow$ $q=-Q/4$