A) 6050
B) 9075
C) 12100
D) 24200
Correct Answer: D
Solution :
\[{{2}^{3}}+{{4}^{3}}+{{6}^{3}}+...+{{20}^{3}}\] \[={{(2\times 1)}^{3}}+{{(2\times 2)}^{3}}+{{(2\times 3)}^{3}}+...+{{(2\times 10)}^{3}}\] \[=8\times {{1}^{3}}+8\times {{2}^{3}}+8\times {{3}^{3}}+...+8\times {{10}^{3}}\] \[=8\times [{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+{{4}^{3}}+...+{{10}^{3}}]\] \[=8\times 3025=24200\] [\[\therefore \]Given,\[{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+{{4}^{3}}+...+{{10}^{3}}=3025\]]
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