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KVPY Sample Paper KVPY Stream-SX Model Paper-8

  • question_answer
    If a, b, c are in G.P., x and y be the arithmetic mean between a, b and b, c respectively, the \[\left( \frac{a}{x}+\frac{c}{y} \right)\,\,\left( \frac{b}{x}+\frac{b}{y} \right)\] is equal to-

    A) 2                                 

    B) \[-\,4\]

    C) 4                                 

    D) 6

    Correct Answer: C

    Solution :

    Let \[b=ar,\]\[c=a{{r}^{2}}\]
    \[x=\frac{a\,\,(1+r)}{2}\]
    \[y=\frac{ar\,\,(1+r)}{2}\]
    \[\left( \frac{a}{x}+\frac{c}{y} \right)\,\,\left( \frac{b}{x}+\frac{b}{y} \right)=\left\{ \frac{a\,\,\times \,\,2}{a\,\,(1\,\,+\,\,r)}+\frac{a{{r}^{2}}\,\,\times \,\,2}{ar\,\,(1\,\,+\,\,r)} \right\}\]
    \[\left\{ \frac{ar\,\,\times \,\,2}{a\,\,(1\,\,+\,\,r)}+\frac{ar\,\,\times \,\,2}{ar\,\,(1+r)} \right\}\]
    \[=\left\{ \frac{2}{1+r}+\frac{2r}{1+r} \right\}\,\,\left\{ \frac{2r}{1+r}+\frac{2}{1+r} \right\}=4\]


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