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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2011

  • question_answer
    On the set of all non-zero reals, an operation is defined as \[a*b=\frac{3ab}{2}.\]in this group, a solution of \[({{2}^{*}}x)*{{3}^{-1}}={{4}^{-1}}\]is

    A)  6                                            

    B)  1            

    C)  1/6                                       

    D)  3/2

    Correct Answer: C

    Solution :

    Given binary operation is \[a*b=\frac{3ab}{2}\]                                    ?... (i) Now  \[2*x=\frac{3}{2}.2x=3x\] [from Eq. (i)]   ?...(ii) and   \[(3x)*\frac{1}{3}=\frac{3}{2}.3x.\frac{1}{3}=\frac{3x}{2}\]      ?..(iii) [from Eq. (i)] Then,     \[(2*x)*\,{{3}^{-1}}={{4}^{-1}}\]                 \[\Rightarrow \]               \[(3x)*\frac{1}{3}=\frac{1}{4}\][from Eq. (ii)] \[\Rightarrow \]               \[\frac{3x}{2}=\frac{1}{4}\]  [from Eq. (iii)] \[\Rightarrow \]               \[x=\frac{1}{6}\]


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