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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Mathematics
Chapter
Binomial Theorem

BITSAT 2021 · Mathematics · Binomial Theorem

Coefficient of x^ 13 in the expansion of (1-x)^ 5 (1+x+x^ 2 +x^ 3...

Coefficient of x13x^{13} in the expansion of (1−x)5(1+x+x2+x3)4(1-x)^{5}\left(1+x+x^{2}+x^{3}\right)^{4} is

Options

  1. A4
  2. B6
  3. C32
  4. D5

Correct answer

A. 4

Step-by-step solution

Expression =(1−x)5⋅(1+x)4(1+x2)4=(1-x)^{5} \cdot(1+x)^{4}\left(1+x^{2}\right)^{4}=(1−x)(1−x2)4(1+x2)4=(1−x)(1−x4)4\begin{array}{l} =(1-x)\left(1-x^{2}\right)^{4}\left(1+x^{2}\right)^{4} \\ =(1-x)\left(1-x^{4}\right)^{4} \end{array}∴\therefore Coefficient of x13=−4C3(−1)3=4x^{13}=-{ }^{4} \mathrm{C}_{3}(-1)^{3}=4
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