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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2003

  • question_answer
    In Z, the set of all integers, the inverse of -7 w.r.t. *defined by \[a*b=a+b+7\] for all \[a,\,b\,\in Z\] is :

    A)  -14                                        

    B)  7

    C)  14                                         

    D)  -7

    Correct Answer: D

    Solution :

    Let e be the identity of Z. Then by given operation \[a*e=a+e+7\]                 \[\Rightarrow \]               \[a=a+e+7\]                       \[[a*e=a]\]                 \[\Rightarrow \]               \[e=-7\] Now inverse of \[-7\]                 \[{{(-7)}^{-1}}={{e}^{-1}}\]                           \[[e=-7]\]                                 \[=e\]                   \[[{{e}^{-1}}=e]\]                             \[=-7\]                  \[[e=-7]\]


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