Among Fe^ 2+ , Fe^ 3+ , Cr^ 2+ and Zn^ 2+ , the ion that shows...

The borax bead test is given by transition metal ions that have unpaired electrons and form coloured compounds.

$Zn^{2+}$ has a completely filled $3d^{10}$ configuration, making it colourless, so it does not give a positive borax bead test.

The remaining ions and their electronic configurations are:
$Fe^{2+} : [Ar] 3d^{6}$
$Cr^{2+} : [Ar] 3d^{4}$
$Fe^{3+} : [Ar] 3d^{5}$

The ionisation enthalpy of an ion refers to the energy required to remove an electron from it. $Fe^{3+}$ has a highly stable half-filled $d$-subshell configuration ($3d^{5}$). Removing an electron from this stable configuration requires significantly more energy compared to removing an electron from $Fe^{2+}$ ($3d^{6}$) or $Cr^{2+}$ ($3d^{4}$).

Therefore, $Fe^{3+}$ shows a positive borax bead test and has the highest ionisation enthalpy among the given ions.

Answer: $Fe^{3+}$