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

  • question_answer
    If \[\mathbf{A}={{\mathbf{2}}^{x}},\mathbf{B}={{\mathbf{4}}^{\mathbf{y}}},\mathbf{C}={{\mathbf{8}}^{z}}\], where \[\mathbf{x}=0.\overline{1},\mathbf{y}=\mathbf{0}.\overline{\mathbf{4}},\mathbf{z}=\mathbf{0}.\overline{\mathbf{6}}\], then \[\mathbf{A}\times \mathbf{B}\times \mathbf{C}\]is

    A)  8       

    B)  2             

    C)  16                               

    D)  4

    Correct Answer: A

    Solution :

    (a): \[A\times B\times C={{2}^{x}}\times {{4}^{y}}\times {{8}^{z}}\] \[\Rightarrow {{2}^{x}}\times {{2}^{y}}\times {{2}^{3x}}\] \[\Rightarrow {{2}^{\left( x+2y+3z \right)}}\Rightarrow {{2}^{\left( \frac{1}{9}+\frac{8}{9}+\frac{18}{9} \right)}}\] \[\Rightarrow {{2}^{3}}=8\]                 


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