2. Solved Papers
  3. BCECE Engineering

BCECE Engineering BCECE Engineering Solved Paper-2007

  • question_answer
    If the second term in the expansion\[{{\left[ \sqrt[13]{a}\frac{a}{\sqrt{{{a}^{-1}}}} \right]}^{n}}\]is \[14{{a}^{5/2}},\] then the value of \[\frac{{{\,}^{n}}C{{\,}_{3}}}{{{\,}^{n}}{{C}_{2}}}\]is

    A)  4                                            

    B)  3                            

    C)         12                         

    D)         6

    Correct Answer: A

    Solution :

    We have, \[{{T}_{2}}=14{{a}^{5/2}}\]                 \[\Rightarrow \]\[{{\,}^{n}}{{C}_{1}}{{({{\alpha }^{1/13}})}^{n-1}}{{({{a}^{3/2}})}^{1}}=14{{a}^{5/2}}\] \[\Rightarrow \]               \[n{{a}^{\frac{n-1}{13}+\frac{3}{2}}}=14{{a}^{5/2}}\] \[\Rightarrow \]               \[n=14\] \[\therefore \]            \[\frac{{{\,}^{n}}{{C}_{3}}}{{{\,}^{n}}{{C}_{2}}}=\frac{{{\,}^{14}}{{C}_{3}}}{{{\,}^{14}}{{C}_{2}}}=\frac{12}{3}=4.\]


You need to login to perform this action.
You will be redirected in 3 sec spinner