JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Properties of binomial coefficients

  • question_answer
    In the expansion of \[{{(1+x)}^{n}}\] the sum of coefficients of odd powers of x is       [MP PET 1986, 93, 2003]

    A) \[{{2}^{n}}+1\]

    B) \[{{2}^{n}}-1\]

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

    D) \[{{2}^{n-1}}\]

    Correct Answer: D

    Solution :

    Sum of the coefficient of odd powers of x \[={{C}_{1}}+{{C}_{3}}+{{C}_{5}}+....={{2}^{n-1}}\]


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