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SSC Sample Paper SSC CGL - Sample Paper-9

  • question_answer
    \[[{{2}^{2}}+{{3}^{2}}+{{4}^{2}}+{{5}^{2}}+{{6}^{2}}+{{7}^{2}}+{{8}^{2}}+{{9}^{2}}+{{10}^{2}}]\] is equal to

    A)  385                             

    B)  2916

    C)  540                             

    D)  384

    Correct Answer: D

    Solution :

    We know that \[{{1}^{2}}+{{2}^{2}}+{{3}^{2}}+......+{{n}^{2}}\]              \[=\frac{n(n+1)(2n+1)}{6}\] \[\therefore \]      \[{{2}^{2}}+{{3}^{2}}+{{4}^{2}}+.....+{{10}^{2}}\]             \[=({{1}^{2}}+{{2}^{2}}+{{3}^{2}}+....+{{10}^{2}})-1\]             \[=\frac{10(10+1)(2\times 10+1)}{6}-1\]             \[=\frac{10\times 11\times 21}{6}-1\]             \[=358-1=384\]


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