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

  • question_answer
    The value of \[^{15}C_{0}^{2}{{-}^{15}}C_{1}^{2}{{+}^{15}}C_{2}^{2}-....{{-}^{15}}C_{15}^{2}\]is [MP PET 1996]

    A) 15

    B) ? 15

    C) 0

    D) 51

    Correct Answer: C

    Solution :

    As we know that \[^{n}{{C}_{0}}-{{\,}^{n}}C_{1}^{2}+{{\,}^{n}}C_{2}^{2}-{{\,}^{n}}C_{3}^{2}+...+{{(-1)}^{n}}.{{\,}^{n}}C_{n}^{2}=0\], (if n is odd) and in the question n=15 (odd).


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