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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2015

  • question_answer
    The length of the longer diagonal of the parallelogram constructed on \[\int{\sqrt{\frac{x}{{{a}^{3}}-{{x}^{3}}}}}dx\] and\[\frac{2}{3}{{\cos }^{-1}}\left( \frac{{{x}^{2/3}}}{{{a}^{2/3}}} \right)+C\], if it is given that)\[\frac{2}{3}{{\tan }^{-1}}\left( \frac{{{x}^{2/3}}}{{{a}^{2/3}}} \right)+C\]and TT. angle between a and b is \[\frac{2}{3}{{\sin }^{-1}}\left( \frac{{{x}^{2/3}}}{{{a}^{2/3}}} \right)+C\], is

    A) \[\frac{2}{3}{{\sin }^{-1}}\left( \frac{{{x}^{3/2}}}{{{a}^{3/2}}} \right)+C\]               

    B)  \[\int{\frac{dx}{({{x}^{2}}+1)({{x}^{2}}+4)}}=k{{\tan }^{-1}}x+1{{\tan }^{-1}}\tan \frac{x}{c}+C\]

    C) \[k=\frac{1}{3},l=-\frac{1}{6}\]                  

    D) 15

    Correct Answer: B

    Solution :

    The diagonals of the parallelogram are \[\text{N}{{\text{a}}_{\text{2}}}{{\text{S}}_{4}}{{\text{O}}_{6}}\] and  \[\text{NaHS}{{\text{O}}_{3}}\] Now, \[\text{Sr}\] \[\text{Sr}\] \[\text{I}\] And        \[\text{C}{{\text{u}}^{\text{2}+}}\] \[\text{C}{{\text{d}}^{\text{2}+}}\] \[\left( \text{Z}=\text{23} \right)\] \[HCl\]


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