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7th Class Mathematics Integers Question Bank Number System

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

    A)  8

    B)  2             

    C)  16                               

    D)  4

    Correct Answer: A

    Solution :

    (a): \[A\times B\times C={{2}^{x}}\times {{\left( {{2}^{2}} \right)}^{y}}\times {{\left( {{2}^{3}} \right)}^{z}}\] \[={{2}^{x+2y+3z}}\] \[\therefore x+2y+3z=\frac{1}{9}+\frac{8}{9}+\frac{18}{9}\] \[=\frac{27}{9}=3\] \[\therefore A\times B\times C={{2}^{3}}=8.\]            


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