$(a)$ Identify the element that has two completely filled shells and the number of valence electrons in each are as: $(i)$ $1$,$(ii)$ $2$,$(iii)$ $7$,$(iv)$ $8$. $(b)$ Analyse which amongst them is inert.

(D) An element with two completely filled shells follows the electronic configuration $(2, 8)$. The total number of electrons is $2 + 8 = 10$,which corresponds to Neon $(Ne)$. The number of valence electrons in this element is $8$.
$(b)$ The element with $8$ valence electrons is inert (noble gas) because its outermost shell is completely filled,making it chemically stable and non-reactive. Thus,the element with $8$ valence electrons is inert.