VIT Engineering VIT Engineering Solved Paper-2014

  • question_answer
    If l (m. n) = \[\int_{0}^{1}{{{t}^{m}}{{\left( 1+t \right)}^{n}}dt,}\] then the expression for l (m, n) in terms of l (m +  n + 1) is

    A) \[\frac{{{2}^{n}}}{m+1}-\frac{n}{m+1}.l\left( m+1,n+1 \right)\]

    B) \[\frac{n}{m+1}.l\left( m+1,n-1 \right)\]

    C) \[\frac{2n}{m+1}+\frac{n}{m+1}l.\left( m+1,n-1 \right)\]

    D) \[\frac{m}{n+1}.l\left( m+1,n-1 \right)\]

    Correct Answer: A

    Solution :

    We have, \[\Delta {{T}_{b}}={{k}_{b}}\] \[\left( {{\text{R}}_{\text{1}}}\text{-X  and  }{{\text{R}}_{\text{2}}}\text{-X} \right)\]          \[T{{l}_{2}}O\]                      \[\frac{X}{m}=\frac{k'p}{1+kp}\]              \[\begin{align}   & OO \\  & |||| \\  & C{{H}_{3}}-C-C{{H}_{2}}-C-O{{C}_{2}}{{H}_{5}}\rightleftharpoons  \\  & \left( keto \right) \\ \end{align}\]


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