Discuss the pattern of variation in the oxidation states of $(i)$ $B$ to $Tl$ and $(ii)$ $C$ to $Pb$.

(N/A) $(i)$ $B$ to $Tl$: The electronic configuration of group $13$ elements is $ns^2 np^1$. Therefore,the most common oxidation state exhibited by them should be $+3$. However,it is only boron and aluminium which practically show the $+3$ oxidation state.
The remaining elements,i.e.,$Ga$,$In$,$Tl$,show both the $+1$ and $+3$ oxidation states. On moving down the group,the $+1$ state becomes more stable. For example,$Tl(+1)$ is more stable than $Tl(+3)$. This is because of the inert pair effect.
The two electrons present in the $s$-shell are strongly attracted by the nucleus and do not participate in bonding. This inert pair effect becomes more and more prominent on moving down the group. Hence,$Ga(+1)$ is unstable,$In(+1)$ is fairly stable and $Tl(+1)$ is very stable.

Elements	$B, Al, Ga, In, Tl$
Oxidation number	$B(+3), Al(+3), Ga(+1, +3), In(+1, +3), Tl(+1, +3)$

The stability of the $+3$ oxidation state decreases on moving down the group.
$(ii)$ $C$ to $Pb$: The electronic configuration of group $14$ elements is $ns^2 np^2$. Therefore,the most common oxidation state exhibited by them should be $+4$. However,the $+2$ oxidation state becomes more and more common on moving down the group. $C$ and $Si$ mostly show the $+4$ state.
On moving down the group,the higher oxidation state becomes less stable. This is because of the inert pair effect. Thus,although $Ge, Sn$ and $Pb$ show both the $+2$ and $+4$ states,the stability of the lower oxidation state increases and that of the higher oxidation state decreases on moving down the group.

Elements	$C, Si, Ge, Sn, Pb$
Oxidation number	$C(+4), Si(+4), Ge(+2, +4), Sn(+2, +4), Pb(+2, +4)$