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Manipal Engineering Manipal Engineering Solved Paper-2011

  • question_answer
    In the group\[G=(\{1,\,\,2,\,\,3,\,\,4\},\,\,{{\times }_{5}})\]the solution of\[{{2}^{-1}}\times (3{{\times }_{5}}x)=4\]is

    A)  1                            

    B)  2

    C)  3                            

    D)         None of these

    Correct Answer: A

    Solution :

                    The composition table is as given below
    \[{{\times }_{5}}\] 1 2 3 4
    1 2 3 4 1 2 3 4 2 4 1 3 3 1 4 2 4 3 2 1
    Clearly, identity element\[=1\] \[\therefore \]       \[{{2}^{-1}}{{\times }_{5}}(3{{\times }_{5}}x)=4\] \[\Rightarrow \]               \[3{{\times }_{5}}(3{{\times }_{5}}x)=4\] \[\Rightarrow \]               \[(3{{\times }_{5}}3){{\times }_{5}}x=4\] \[\Rightarrow \]                         \[4{{\times }_{5}}x=4\] \[\Rightarrow \]               \[x={{4}^{-1}}{{\times }_{5}}4=1\]


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