JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Critical Thinking Questions

  • question_answer The value of \[{{2}^{n}}\,\{1.3.5.....(2n-3)\,(2n-1)\}\] is

    A) \[\frac{(2n)\,!}{n\,!}\]

    B) \[\frac{(2n)\,!}{{{2}^{n}}}\]

    C) \[{{2}^{n-i}}\]

    D) None of these

    Correct Answer: A

    Solution :

    \[1\ .\ 3\ .\ 5......(2n-1)\,{{2}^{n}}\]\[=\frac{1\,.\,2\,.\,3\,.\,4.\,5.\,6....(2n-1)\,(2n)\,{{2}^{n}}}{2.\,4.\,6.....2n}\] \[=\frac{(2n)\,!\ {{2}^{n}}}{{{2}^{n}}(1\ .\ 2\ .\ 3......n)}=\frac{(2n)\ !}{n\ !}\].


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