(i)-(b), (ii)-(d),(iii)-(a),(iv)-(e),(v)- (c)

(i)-(b) Ce- [Xe]4f¹ 5d¹ 6s². Cerium can lose all 4 electrons so as to attain noble gas configuration.So, oxidation state of Ce is +4

(ii)-(d) Eu- [Xe]4f⁷ 5d⁰ 6s².Europium can show +2 and +3 oxidation states.

(iii)-(a) Promethium is a radioactive lanthanoid.

(iv)-(e)Gd-[Xe]4f⁷ 5d¹ 6s². Gadolinium shows oxidation state of +3.

(v) –(c) Lu-[Xe]4f¹⁴ 5d¹ 6s². Lutetium has a 4f¹⁴ electronic configuration and a +3 oxidation state.