Which of the following does not correctly represent the order of the property indicated against it?

The magnetic moment depends on the number of unpaired electrons. The electronic configurations of the given ions are $\text{Ti}^{3+}$ ($3d^{1}$), $\text{V}^{3+}$ ($3d^{2}$), $\text{Cr}^{3+}$ ($3d^{3}$), and $\text{Mn}^{3+}$ ($3d^{4}$). The number of unpaired electrons increases from 1 to 4, so the magnetic moment increases in the order $\text{Ti}^{3+} < \text{V}^{3+} < \text{Cr}^{3+} < \text{Mn}^{3+}$.

The highest oxidation states shown by the elements are Ti (+4), V (+5), Cr (+6), and Mn (+7). The order $\text{Ti} < \text{V} < \text{Cr} < \text{Mn}$ is correct.

The melting point of transition metals depends on the strength of metallic bonding, which is related to the number of unpaired electrons. However, Mn has an anomalously low melting point due to its stable half-filled $3d^{5}$ configuration, which results in weaker interatomic interactions. The correct order of melting points is $\text{Mn} < \text{Ti} < \text{Cr} < \text{V}$. Thus, the given order $\text{Ti} < \text{V} < \text{Cr} < \text{Mn}$ is incorrect.

The second ionisation enthalpy involves the removal of an electron from the $M^{+}$ ion. The electronic configurations of the $M^{+}$ ions are $\text{Ti}^{+}$ ($3d^{2}4s^{1}$), $\text{V}^{+}$ ($3d^{3}4s^{1}$), $\text{Cr}^{+}$ ($3d^{5}$), and $\text{Mn}^{+}$ ($3d^{5}4s^{1}$). Removing an electron from $\text{Cr}^{+}$ requires breaking the highly stable half-filled $3d^{5}$ configuration, making its second ionisation enthalpy the highest among them. The correct order is $\text{Ti} < \text{V} < \text{Mn} < \text{Cr}$.

Answer: $\text{Ti} < \text{V} < \text{Cr} < \text{Mn}$ [Increasing order of melting point]