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SSC Sample Paper SSC CHSL (10+2) Sample Test Paper-4

  • question_answer
    \[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+.....+\frac{1}{\sqrt{7}+\sqrt{8}}\]\[+\frac{1}{\sqrt{8}+\sqrt{9}}=?\]

    A)  0                                

    B)  1

    C)  2           

    D)  4

    Correct Answer: C

    Solution :

                 Rationalising the denominator of each term, Expression \[=\frac{1-\sqrt{2}}{1-2}+\frac{\sqrt{2}-\sqrt{3}}{2-3}+\frac{\sqrt{3}-\sqrt{4}}{3-4}+....+\frac{\sqrt{7}-\sqrt{8}}{7-8}\]\[+\frac{\sqrt{8}-\sqrt{9}}{8-9}\] \[=1+\sqrt{2}-\sqrt{2}+\sqrt{3}-\sqrt{3}+\sqrt{4}-\sqrt{4}\] \[+\sqrt{5}-\sqrt{5}+\sqrt{6}-\sqrt{6}+\sqrt{7}-\sqrt{7}+\sqrt{8}-\sqrt{8}+\sqrt{9}\] \[=1+\sqrt{9}=-1+3=2\]


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