The ions which are arranged in correct order of increasing radii are

We know that Atomic and Ionic radii of Anion is greater than Cation

In case of cation as charge increases size decreases.

Now , In  Option (a) ${\mathrm{K}}^{+},{\mathrm{Ca}}^{2+},{\mathrm{S}}^{2-}$ we can can see that Calcium has more charge than Potassium that is why it is incorrect.

 In option(b) ${\mathrm{Be}}^{2+},{\mathrm{Mg}}^{2+},{\mathrm{Na}}^{+}$

We know that as we move along from Be to Mg atomic radii increases, therefore it is correct.

Hence, option(b) is the correct answer.