How many of the following metal ions have similar value of spin only magnetic moment in gaseous state?…

From magnetic moment formula:
${\mu }_{\mathrm{s}}=\sqrt{\mathrm{n}(\mathrm{n}+2)}\mathrm{BM} (\mathrm{n}=$ no. of unpaired electrons )

Ion           E.C.            n
${\mathrm{V}}^{3+}:\left[\mathrm{Ar}\right]3 {\mathrm{d}}^{2}4 {\mathrm{s}}^0 2$

${\mathrm{Cr}}^{3+}:\left[\mathrm{Ar}\right]3 {\mathrm{d}}^{3}4 {\mathrm{s}}^0 3$

${\mathrm{Fe}}^{2+}:\left[\mathrm{Ar}\right]3 {\mathrm{d}}^{6}4 {\mathrm{s}}^0 4$

${\mathrm{Ni}}^{3+}:\left[\mathrm{Ar}\right]3 {\mathrm{d}}^{7}4 {\mathrm{s}}^0 3$

Thus, ${\mathrm{Cr}}^{3+}\&{\mathrm{Ni}}^{3+}$ have same value of ${\mu }_{\mathrm{s}}$