A) 4235
B) 5050
C) 7700
D) None of these
Correct Answer: C
Solution :
[c] \[\sum\limits_{n=1}^{10}{\sum\limits_{m=1}^{10}{({{m}^{2}}+{{n}^{2}})}}\] \[=\sum\limits_{n=1}^{10}{[({{1}^{2}}+{{n}^{2}})+({{2}^{2}}+{{n}^{2}})+....+({{10}^{2}}+{{n}^{2}})]}\] \[=10[{{(1)}^{2}}+{{(2)}^{2}}+....+{{(10)}^{2}}]+10[{{(1)}^{2}}\] \[+{{(2)}^{2}}+....+{{(10)}^{2}}]\] \[=\frac{20.10.11.21}{6}=7700\]
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