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SSC Sample Paper SSC CGL - Sample Paper-20

  • question_answer
    \[\left( \frac{3\sqrt{2}}{\sqrt{6}-\sqrt{3}}-\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}}-\frac{6}{\sqrt{8}+\sqrt{12}} \right)\] is equal to

    A) 1                                 

    B) \[-\sqrt{3}\]

    C) \[\sqrt{3}+\sqrt{2}\]                  

    D) \[\sqrt{3}-\sqrt{2}\]

    Correct Answer: B

    Solution :

    \[\frac{3\sqrt{2}}{\sqrt{6}-\sqrt{3}}-\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}}-\frac{6}{2\sqrt{2}+2\sqrt{3}}\] \[=\frac{3\sqrt{2}(\sqrt{6}+\sqrt{3})}{\sqrt{6}-\sqrt{3}}-\frac{4\sqrt{3}(\sqrt{6}+\sqrt{2})}{\sqrt{6}-\sqrt{2}}\]\[-\frac{3(\sqrt{3}-\sqrt{2)}}{3-2}\] \[=\sqrt{2}(\sqrt{6}+\sqrt{3})-\sqrt{3}(\sqrt{6}+\sqrt{2})-3(\sqrt{3}-\sqrt{2)}\] \[=\sqrt{12}+\sqrt{6}-\sqrt{18}-\sqrt{6}-3\sqrt{3}+3\sqrt{2}\] \[=2\sqrt{3}-3\sqrt{2}-3\sqrt{3}+3\sqrt{2}\] \[=-\sqrt{3}\]


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