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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

  • question_answer
    If p and q be positive, then the coefficients of \[{{x}^{p}}\] and \[{{x}^{q}}\] in the expansion of \[{{(1+x)}^{p+q}}\]will be [MNR 1983; AIEEE 2002]

    A) Equal

    B) Equal in magnitude but opposite in sign

    C) Reciprocal to each other

    D) None of these

    Correct Answer: A

    Solution :

    Coefficient of \[{{x}^{p}}\] is \[^{(p+q)}{{C}_{p}}\] and coefficient of \[{{x}^{q}}\] is \[^{(p+q)}{{C}_{q}}\].  But \[^{(p+q)}{{C}_{p}}={{\,}^{(p+q)}}{{C}_{q}}\], \[(\because {{\,}^{n}}{{C}_{r}}={{\,}^{n}}{{C}_{n-r}})\].


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