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KVPY Sample Paper KVPY Stream-SX Model Paper-2

  • question_answer
    \[\int\limits_{-1}^{1}{\frac{{{x}^{3}}+|x|+1}{{{x}^{2}}+2|x|+1}dx=a/n\,\,2+b}\] then:

    A) \[a=2;\]\[b=1\]              

    B) \[a=2;\]\[b=0\]

    C) \[a=3;\]\[b=-\,2\]           

    D) \[a=4;\]\[b=-1\]

    Correct Answer: B

    Solution :

    \[l=\int\limits_{-1}^{1}{\frac{{{x}^{3}}}{{{x}^{2}}+2|x|+1}\,\,dx+\int\limits_{-1}^{1}{\frac{|x|+1}{{{(|x|+1)}^{2}}}dx}}\] \[\Rightarrow \]   \[2\int\limits_{0}^{1}{\frac{dx}{1+x}}=2/n\,\,2\] [odd \[\Rightarrow \]vanishes even]


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