(a)
Ions $\ \ \ \ \ \ \ \ \ \ \ \ \ \ Be^{2 +}\ \ Cl^{-}\ \ S^{2 -}\ \ Na^{+}\ \ Mg^{2 +}\ \ Br^{-}$
Valence shell 1 3 3 2 2 4
Now, between $Na^{+}\ and\ Mg^{2 +},\ Na^{+} > Mg^{2 +}$ (isoelectronic), between $Cl^{-}\ and\ S^{2 -},\ S^{2 -} > Cl^{-}$ (isoelectronic) because for isoelectronic species size decreases as the atomic number increases. Hence, the order of increasing size is
$Be^{2 +} > \ Mg^{2 +} > \ Na^{+} > Cl^{-} > S^{2 -} > Br^{-}$