A) \[1500\]
B) \[1800\]
C) \[2100\]
D) \[2400\]
Correct Answer: C
Solution :
[c] \[{{11}^{2}}-{{1}^{2}}+{{12}^{2}}-{{2}^{2}}+{{13}^{3}}-{{3}^{2}}+...+{{20}^{2}}-{{10}^{2}}\] \[=({{1}^{2}}+{{2}^{2}}+{{3}^{2}}+....+{{20}^{2}})-2({{1}^{2}}+{{2}^{2}}+{{3}^{2}}+...+{{10}^{2}})\]\[=\frac{20\times 21\times 41}{6}-2\times \frac{10\times 11\times 21}{6}\] \[=\frac{420}{6}\,(41-11)=2100\]
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