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KVPY Sample Paper KVPY Stream-SX Model Paper-16

  • question_answer
    If A(n) represents the area bounded by the curve \[y=n.\ell nx,\] where \[n\,\,\in \,\,N\] and n > 1, the x-axis and the lines x = 1 and x = e, then the value of \[A(n)+nA(n-1)\] is equal to -

    A) \[\frac{{{n}^{2}}}{e+1}\]

    B) \[\frac{{{n}^{2}}}{e-1}\]

    C) \[{{n}^{2}}\]

    D) \[e{{n}^{2}}\]

    Correct Answer: C

    Solution :

    \[y=n\,\ell n\,x,\] \[n>1,\] \[n\in N\]
    \[A\,(n)=\int\limits_{1}^{e}{n\ell nxdx=n}\]
    \[\therefore \,\,A\,(n)+n\,A\,(n-1)={{n}^{2}}.\]


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