A positive charge $Q$ is uniformly distributed along a circular ring of radius $R$. A small test charge $q$ is placed at the centre of the ring as shown in figure. Then 

At the centre of the ring, $E = 0$. When a positive charge $q>0$ is displaced away from the centre in the plane of the ring, say to the right, force of repulsion on $q$, due to charge on right half increases and due to charge on left half decreases. Therefore, charge $q$ is pushed back towards the centre. So option $\left(a\right)$ is correct. 

When charge $q$ is negative $(q<0)$, force is of attraction. Therefore, charge $q$ displaced to the right continues moving to the right till it hits the ring.

Along the axis of the ring, at a distance $r$ from the centre,

$E=\frac{Qr}{4\pi {\epsilon }_0{(r^2+a^2)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

If charge $q$ is negative $(q<0)$, it will perform SHM for small displacement along the axis.