JEE Main & Advanced Sample Paper JEE Main Sample Paper-21

  • question_answer
    Median of \[^{2n}{{C}_{0,}}^{2n}{{C}_{1,}}^{2n}{{C}_{2,}}^{2n}{{C}_{3,}}{{.......}^{2n}}{{C}_{n,}}\] (where n is even) is \[[note:{{}^{n}}{{C}_{r}}=\frac{n!}{r!(n-r)!}]\]

    A)  \[^{2n}{{C}_{\frac{n}{2}}}\]                         

    B)   \[^{2n}{{C}_{\frac{n+1}{2}}}\]

    C)  \[^{2n}{{C}_{\frac{n-1}{2}}}\]                      

    D)  \[^{2n}{{C}_{n}}\]

    Correct Answer: A

    Solution :

    Total number of terms \[=n+1=\] odd \[\therefore \] median \[=\frac{n+1+1}{2}\Rightarrow \,{{\left( \frac{n}{2}+1 \right)}^{th}}\] term \[\Rightarrow \,{{\,}^{2n}}{{C}_{\frac{n}{2}}}\]


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