Which of the following lanthanoid elements exhibits $+2$ and $+3$ oxidation states?

Arrange the following metal complexes/compounds in the increasing order of spin-only magnetic moment. Presume all three are high-spin systems.
(Atomic numbers: $Ce = 58$,$Gd = 64$,and $Eu = 63$.)
$(a)$ $(NH_4)_2[Ce(NO_3)_6]$
$(b)$ $Gd(NO_3)_3$
$(c)$ $Eu(NO_3)_3$
Answer is:

Which element from the following has a half-filled $f$ orbital in the $+3$ oxidation state?

Which of the following is $NOT$ a lanthanoid element?

The total number of rare-earth elements is

If the electronic configuration of $M^{3+}$ is $[Xe] \ 4f^3$,then $M^{3+}$ is