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7th Class Mental Ability Algebraic Expressions Question Bank Algebra

  • question_answer
    The value of \[\frac{{{\mathbf{2}}^{\mathbf{x+3}}}\mathbf{\times }{{\mathbf{3}}^{\mathbf{2x-y}}}\mathbf{\times }{{\mathbf{5}}^{\mathbf{x+y+3}}}\mathbf{\times }{{\mathbf{6}}^{\mathbf{y+1}}}}{{{\mathbf{6}}^{\mathbf{x+1}}}\mathbf{\times 1}{{\mathbf{0}}^{\mathbf{y+3}}}\mathbf{\times 1}{{\mathbf{5}}^{\mathbf{x}}}}\]is:

    A) 1    

    B)                           0

    C) -1              

    D)               10

    E) None of these

    Correct Answer: A

    Solution :

    Explanation \[=\,\,\,\frac{{{2}^{x+3}}\times {{3}^{2x-y}}\times {{5}^{x+y+3}}\times \,\,{{6}^{y\,+\,1}}}{{{6}^{x\,+\,1}}\times {{10}^{y\,+\,3}}\times {{15}^{x}}}\] \[=\,\,\,\frac{{{2}^{x+3}}\times {{3}^{2x-y}}\times {{5}^{x+y+3}}\times \,\,{{(2\times 3)}^{y\,+\,1}}}{{{(2\times 3)}^{x\,+\,1}}\times {{(5\times 2)}^{y\,+\,3}}\times {{(5\times 3)}^{x}}}\] \[=\,\,\,\frac{{{2}^{x+3}}\times {{3}^{2x-y}}\times {{5}^{x+y+3}}\times \,\,{{2}^{y\,+\,1}}\times {{3}^{y\,+\,1}}}{{{2}^{x\,+\,1}}\times {{3}^{x\,+\,1}}\times {{5}^{y\,+\,3}}\times {{2}^{y\,+\,3}}\times {{5}^{x}}\times {{3}^{x}}}\] \[=\,\,\frac{{{2}^{x+y+4}}\times {{3}^{2x\,+\,1}}\times {{5}^{x\,+\,y\,+\,3}}}{{{2}^{x+y+4}}\times {{3}^{2x+1}}\times {{5}^{x+y+3}}}=1\]          


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