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Railways Sample Paper RRBs Assistant Loco Pilot and Technician CBT STAGE-I Sample Paper-33

  • question_answer
    The sum of\[\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}\] \[+\frac{1}{\sqrt{4}+\sqrt{3}}...+\frac{1}{\sqrt{100}+\sqrt{99}}\]is

    A)  9

    B)                     10

    C)  11                   

    D)  None of the above

    Correct Answer: A

    Solution :

    \[\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+...+\frac{1}{\sqrt{100}+\sqrt{99}}\] \[=\sqrt{2}-1+\sqrt{3}-\sqrt{2}+...+\sqrt{100}-\sqrt{99}\] \[=10-1=9\]


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