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Railways Sample Paper RRBs Assistant Loco Pilot and Technician CBT STAGE-I Sample Paper-1

  • question_answer
    The sum \[({{5}^{3}}+{{6}^{3}}+...+{{10}^{3}})\]is equal to

    A)  2295   

    B)  2425

    C)  2495               

    D)  2925

    Correct Answer: D

    Solution :

    \[{{5}^{3}}\,+{{6}^{3}}\,+...+{{10}^{3}}\] \[={{1}^{3}}\,+\,{{2}^{3}}\,+...+{{10}^{3}}\,-\left( {{1}^{3}}+{{2}^{3}}+{{3}^{3}}+{{4}^{3}} \right)\] \[={{\left\{ \frac{10\left( 10+1 \right)}{2} \right\}}^{2}}\,-\,{{\left\{ \frac{4\left( 4+1 \right)}{2} \right\}}^{2}}\] \[=\,3025-100=2925\]


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