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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2000

  • 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)         \[\frac{1}{3}\]

    E)  \[\frac{2}{3}\]

    Correct Answer: A

    Solution :

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


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