A) \[10\times (11!)\]
B) \[101\times (10!)\]
C) \[(11!)\]
D) \[11\times (11!)\]
Correct Answer: A
Solution :
\[\sum\limits_{r=1}^{10}{\left\{ {{({{r}^{2}}+1)}^{2}} \right\}.r\,\,!}\] \[=\sum\limits_{r=1}^{10}{\left\{ {{(r+1)}^{2}}-2r \right\}r\,\,!}\] \[=\,\,\sum\limits_{r=1}^{10}{(r+1)(r+1)!-2}\sum\limits_{r=1}^{10}{r.r!}\] \[=\,(11.11!-1-(11!\tilde{\ }1!)\] \[=\,10.11!\]
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