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NTSE Sample Paper NTSE SAT Practice Test-9

  • question_answer
    The expression \[\frac{{{\left( x+\frac{1}{y} \right)}^{a}}{{\left( x-\frac{1}{y} \right)}^{b}}}{{{\left( y+\frac{1}{x} \right)}^{a}}{{\left( y-\frac{1}{x} \right)}^{b}}}\] reduces to      

    A) \[{{\left( \frac{y}{x} \right)}^{a+b}}\]              

    B)  \[{{\left( \frac{x}{y} \right)}^{a+b}}\]

    C)              \[{{\left( \frac{y}{x} \right)}^{a-b}}\]               

    D) \[{{\left( \frac{x}{y} \right)}^{a-b}}\]  

    Correct Answer: B

    Solution :

    [b] Given expression \[=\frac{{{\left( \frac{xy+1}{y} \right)}^{a}}{{\left( \frac{xy-1}{y} \right)}^{b}}}{{{\left( \frac{xy+1}{x} \right)}^{a}}{{\left( \frac{xy-1}{x} \right)}^{b}}}\] \[\frac{{{x}^{a}}}{{{y}^{a}}}.\frac{{{x}^{b}}}{{{y}^{b}}}={{\left( \frac{x}{y} \right)}^{a+b}}\]


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