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JEE Main & Advanced Sample Paper JEE Main Sample Paper-27

  • question_answer
    Let G be the geometric mean of two positive numbers a and b, and M be the arithmetic mean of \[\frac{1}{a}\] and \[\frac{1}{b}\]. If \[\frac{1}{M}:G\] is \[4:5\], then \[a:b\] can be

    A)  \[2:3\]                                      

    B)  \[1:4\]

    C)  \[1:2\]                                      

    D)  \[3:4\]  

    Correct Answer: B

    Solution :

    \[G=\sqrt{ab};\,\,M=\left( \frac{\frac{1}{a}+\frac{1}{b}}{2} \right)\Rightarrow \,\frac{1}{M}=\,\left( \frac{2}{\frac{1}{a}+\frac{1}{b}} \right)\] Now, \[\frac{1}{M}\div G=4:5\] \[\Rightarrow \,\,\sqrt{\frac{a}{b}}+\frac{b}{a}\,=\frac{5}{2}\] \[\Rightarrow \,\,\sqrt{\frac{a}{b}}\,=\frac{2}{1}\,\,or\,\,\frac{1}{2}\] \[\Rightarrow \,\,\,a:b=4\,:1\,\,\,or\,\,1:4\]


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