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KVPY Sample Paper KVPY Stream-SX Model Paper-2

  • 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 \[A\,(n)+n\,A\,(n-1)\] 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 :

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


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