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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2006

  • question_answer
    In the group G = {1,5,7,11} under multiplication modulo 12, the solution of\[{{7}^{-1}}{{\otimes }_{12}}\,(x\,{{\otimes }_{12}}11)=5\] is equals :

    A)  5                                            

    B)  1

    C)  7                                            

    D)  11

    Correct Answer: B

    Solution :

    Given that \[G=\{1,5,7,11\}\]   is   a   group   under multiplication modulo 12. \[\therefore \]  \[{{7}^{-1}}=7\]                 ( \[\because \] \[{{7}^{-1}}{{\otimes }_{12}}\,7=1\]) Now,    \[{{7}^{-1}}{{\otimes }_{12}}(11{{\otimes }_{12}}x)=5\] \[\Rightarrow \]               \[7{{\otimes }_{12}}(11{{\otimes }_{12}}x)=5\] \[\Rightarrow \]               \[(7{{\otimes }_{12}}11){{\otimes }_{12}}\,x=5\] \[\Rightarrow \]               \[5{{\otimes }_{12}}x=5\] \[\Rightarrow \]               \[x=1\]


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