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Manipal Engineering Manipal Engineering Solved Paper-2013

  • question_answer
    \[G\]is a set of all rational numbers except\[-1\]and\[*\]is defined by\[a*b=a+b+ab\]for all\[a,\,\,b\in G\], in the group\[(G,\,\,*)\], the solution of \[{{2}^{-1}}*\,x*\,{{3}^{-1}}=5\] is

    A) \[71\]                                   

    B) \[68\]

    C) \[63/5\]               

    D)        \[72/5\]

    Correct Answer: A

    Solution :

    \[{{2}^{-1}}*x*{{3}^{-1}}=5\] \[\Rightarrow \]               \[x=2*(5*3)=2*(5+3+15)\]                    \[=2*(23)=2+23+46=71\]


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