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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2004

  • question_answer
    If \[{{Q}_{1}}\] is the set of all relations other than 1 with the binary operation * defined by \[a\,*b=a+b-ab\] for all a, b in \[{{Q}_{1}}\], then the identity in \[{{Q}_{1}}\] with respect to * is :

    A)  1                                            

    B)  0

    C)  -1                                          

    D)  2

    Correct Answer: B

    Solution :

    We know that \[a*I=a\], where \[I\] is the identity. This condition is only satisfied by zero with respect. \[i.e.,\,\,a*0=a+0-0=a\,\,\forall \,\,a,\,0\in {{Q}_{1}}\]then, the identity in \[{{Q}_{1}}\] with is 0


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