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JCECE Engineering JCECE Engineering Solved Paper-2011

  • question_answer
    In the expansion of\[{{(1+x)}^{50}}\], the sum of the coefficients of odd powers of \[x\] is

    A) \[0\]                                     

    B) \[{{2}^{49}}\]

    C) \[{{2}^{50}}\]                                    

    D) \[{{2}^{51}}\]

    Correct Answer: B

    Solution :

    We have\[,\]\[{{(1+x)}^{50}}=\sum\limits_{r=0}^{50}{^{50}{{C}_{r}}{{x}^{r}}}\]. Therefore sum of the coefficients of odd powers of\[x\].                 \[{{=}^{50}}{{C}_{1}}{{+}^{5}}{{C}_{3}}+...{{+}^{50}}{{C}_{49}}={{2}^{50-1}}\]                 \[={{2}^{49}}\]


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