JEE Main & Advanced Sample Paper JEE Main - Mock Test - 19

  • question_answer
    The relation gives the value of P as \[P=\frac{\sqrt{abc}}{7d}.\]. Find the percentage error in P if the percentage error in a, b, c and d are \[2%,\text{ }2%,\text{ }2%\] and \[4%\] respectively

    A) \[\pm 7%\]   

    B)                    \[\pm 5%\]

    C) \[\pm 9%\]              

    D)        \[\pm 8%\]

    Correct Answer: A

    Solution :

    \[\frac{\Delta P}{P}=\pm \left[ \frac{1}{2}\frac{\Delta a}{a}+\frac{1}{2}\frac{\Delta b}{b}+\frac{1}{2}\frac{\Delta C}{c}+\frac{\Delta d}{d} \right]\] \[\Rightarrow \,\,\frac{\Delta P}{P}\times 100=\pm \left[ \frac{1}{2}\times 2%+\frac{1}{2}2%+\frac{1}{2}2%+4% \right]\] \[=\pm [1%+1%+1%+4%]=\pm 7%\]


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