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SSC Sample Paper Mock Test-7 SSC CGL Tear-II Paper-1

  • question_answer
    \[\left[ \frac{1}{\sqrt{2}+\sqrt{3}-\sqrt{5}}+\frac{1}{\sqrt{2}-\sqrt{3}-\sqrt{5}} \right]\] in simplified form equals to    

    A)                   1

    B)  \[\sqrt{2}\]

    C)  \[\frac{1}{\sqrt{2}}\]

    D)  0

    Correct Answer: C

    Solution :

    \[\frac{1}{\sqrt{2}+\sqrt{3}-\sqrt{5}}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{5}}{[\sqrt{2}+\sqrt{3}+\sqrt{5}]}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{5}}{2+3+2\sqrt{6}-5}\]
    \[=\frac{\sqrt{2}+\sqrt{3}+\sqrt{5}}{2\sqrt{6}}\]
    Similarly, \[=\frac{1}{\sqrt{2}-\sqrt{3}-\sqrt{5}}\]
    \[=\frac{\sqrt{2}-\sqrt{3}+\sqrt{5}}{[(\sqrt{2}-\sqrt{3})-\sqrt{5}](\sqrt{2}-\sqrt{3})+\sqrt{5}}\]
    \[=\frac{\sqrt{2}-\sqrt{3}+\sqrt{5}}{-\,\,2\sqrt{6}}\]
    Expression\[=\frac{\sqrt{2}+\sqrt{3}+\sqrt{5}}{2\sqrt{6}}-\frac{\sqrt{2}-\sqrt{3}+\sqrt{5}}{2\sqrt{6}}\]
    \[=\frac{\sqrt{2}+\sqrt{3}+\sqrt{5}-\sqrt{2}+\sqrt{3}-\sqrt{5}}{2\sqrt{6}}\]
    \[=\frac{\sqrt{3}}{\sqrt{6}}=\frac{1}{\sqrt{2}}\]


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