Consider the hydrated ions of

Electronic configuration of the given transition metal ions are :

$\mathrm{Sc}^{3+}(\mathrm{Z}=21) 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6}$

$\mathrm{Ti}^{2+}(\mathrm{Z}=22) 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{2}$

$\mathrm{Ti}^{3+}(\mathrm{Z}=22) 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{1}$

$\mathrm{~V}^{2+}(\mathrm{Z}=23) 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{3}$

Since, magnetic moment is directly proportional to the number of unpaired electrons. The correct increasing order of magnetic moment is $\mathrm{Sc}^{3+}<\mathrm{Ti}^{3+}<\mathrm{Ti}^{2+}<\mathrm{V}^{2+}$ because they have $0,1,2$ and 3 unpaired electrons respectively.