J & K CET Engineering J and K - CET Engineering Solved Paper-2014

  • question_answer Determine n, if \[^{2n}{{C}_{2}}{{:}^{n}}{{C}_{2}}:\,\,\,\,=\,\,9:2\]

    A)  \[5\]      

    B)  \[4\]       

    C)  \[3\]       

    D)  \[2\]

    Correct Answer: A

    Solution :

    Given,  \[^{20}{{C}_{2}}{{:}^{n}}{{C}_{2}}=9:2\] \[\Rightarrow \] \[\frac{^{20}{{C}_{2}}}{^{n}{{C}_{2}}}=\frac{9}{2}\] \[\Rightarrow \] \[\frac{(2n)!}{2!(2n-2)!}\times \frac{2!(n-2)!}{n!}=\frac{9}{2}\] \[\Rightarrow \]\[\frac{(2n)(2n-1)(2n-2)!}{2(2n-2)!}\times \frac{2(n-2)!}{n(n-1)(n-2)!}=\frac{9}{2}\] \[\Rightarrow \] \[\frac{2(2n-1)}{n-1}=\frac{9}{2}\] \[\Rightarrow \] \[4(2n-1)=9(n-1)\] \[\Rightarrow \] \[8n-4=9n-9\] \[\Rightarrow \] \[9n-8n=-4+9\] \[\Rightarrow \] \[n=5\]

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