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Manipal Engineering Manipal Engineering Solved Paper-2012

  • question_answer
    In the set\[{{Q}^{+}}\]of all positive rational numbers, the operation\[*\]is defined by the formula\[a+b=\frac{ab}{6}\]. Then, the inverse of\[9\]with respect to\[*\]is

    A) \[4\]                                     

    B) \[3\]

    C) \[\frac{1}{9}\]                   

    D)        \[\frac{1}{3}\]

    Correct Answer: A

    Solution :

    Let\[e\]be the identity, \[\therefore \]  \[a*e=a\] \[\Rightarrow \]                  \[\frac{ae}{6}=a\] \[\Rightarrow \]                     \[e=6\] \[\because \]        \[a*{{a}^{-1}}=e\] \[\therefore \]        \[a*{{a}^{-1}}=6\] \[\Rightarrow \]               \[\frac{a{{a}^{-1}}}{6}=6\] \[\Rightarrow \]                   \[{{a}^{-1}}=\frac{6\times 6}{a}\] \[\therefore \]       \[{{9}^{-1}}=\frac{6\times 6}{9}=4\]


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