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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2010

  • question_answer
    For\[a,b\in R,\]define\[a*b=\frac{a}{a+b},\]where. \[a+b\ne 0.\]If\[a*b=5,\]then the value of\[b*a\]is

    A)  5   

    B)                                         \[-5\]

    C)  4                            

    D)         \[-7\]

    E)  \[-4\]

    Correct Answer: E

    Solution :

    We have \[a*b=\frac{a}{a+b}\] \[\Rightarrow \]               \[\frac{1}{a*b}=\frac{a+b}{a}=1+\frac{b}{a}\] \[\Rightarrow \]               \[\frac{1}{5}=1+\frac{b}{a}\] \[\Rightarrow \]               \[\frac{b}{a}=-\frac{4}{5}\] \[\Rightarrow \]               \[\frac{a}{b}=-\frac{5}{4}\] Now,     \[\frac{1}{b*a}=\frac{b+a}{b}=1+\frac{a}{b}\]                 \[=1-\frac{5}{4}=-\frac{1}{4}\] \[\Rightarrow \]               \[b*a=-4\]


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