9th Class Mathematics Number System and its Operations Question Bank Number System

  • question_answer
    \[\frac{\mathbf{1}}{\mathbf{1+}{{\mathbf{2}}^{\mathbf{x-y}}}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{1+}{{\mathbf{2}}^{\mathbf{y-x}}}}\mathbf{=?}\]

    A)  \[x\]                            

    B)  \[x-y\]         

    C)  1   

    D)  0

    Correct Answer: C

    Solution :

    (c): \[\frac{1}{1+{{2}^{x-y}}}+\frac{1}{1+{{2}^{y-x}}}\Rightarrow \frac{1}{1+\frac{{{2}^{x}}}{{{2}^{y}}}}+\frac{1}{1+\frac{{{2}^{y}}}{{{2}^{x}}}}\] \[\Rightarrow \frac{{{2}^{y}}}{{{2}^{y}}+{{2}^{x}}}+\frac{{{2}^{x}}}{{{2}^{y}}+{{2}^{y}}}=\frac{{{2}^{x}}+{{2}^{y}}}{{{2}^{x}}+{{2}^{y}}}=1\]                                 


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