Let $S_n=1^2+2\cdot 2^2+3^2+2\cdot 4^2+5^2+2\cdot 6^2+\mathrm{...}\text{'}n\text{'}terms$ . Column-II contains the units digit of the term given in Column-I.

	Column-I		Column-II
(I)	$\frac{3S_{2024}}{506}$	(P)	$6$
(II)	$\frac{3S_{2023}}{506}$	(Q)	$4$
(III)	$\frac{6S_{2022}}{1011}$	(R)	$0$
(IV)	$\frac{6S_{2021}}{1011}$	(S)	$2$

 $S_n=(1^2+2^2+3^2\mathrm{........})+(2^2+4^2+6^2\mathrm{.....})=S_1+S_2$
Case (I): When ‘n’ is even say n=2m, $m\in N$  In this $S_1$  contains m terms and $S_2$ contain m terms 
$S_n=\frac{n(n+1)(2n+1)}{6}+\frac{n(n+2)(n+1)}{6}=\frac{n{(n+1)}^2}{2}$ 
Case (II): When ‘n’ is odd say n=2m+1, $m\in N$  In this  $S_1$  contains (m+1) terms and $S_2$  contain m terms 
$S_n=\frac{n(n+1)(2n+1)}{6}+\frac{(n^2-1)\left(n\right)}{6}=\frac{n^2(n+1)}{2}$