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BITSAT 2012

Exam: BITSAT
Year: 2012
Subject: Mathematics
Chapter: Binomial Theorem

BITSAT 2012 · Mathematics · Binomial Theorem

The coefficient of x^ 20 in the expansion of (1+x^ 2 )^ 40 · (x^ 2...

The coefficient of

x^{20}

in the expansion of

\left(1+x^{2}\right)^{40} \cdot \left(x^{2}+2+\frac{1}{x^{2}}\right)^{-5} is

Options

A ${ }^{30} \mathrm{C}_{10}$
B ${ }^{30} \mathrm{C}_{25}$
C1
DNone of these

Correct answer

B. ${ }^{30} \mathrm{C}_{25}$

Step-by-step solution

Expression

=\left(1+x^{2}\right)^{40} \cdot\left(x+\frac{1}{x}\right)^{-10}=\left(1+x^{2}\right)^{30} \cdot x^{10}

The coefficient of

x^{20} in x^{10}\left(1+x^{2}\right)^{30}=

the coefficient of

\mathrmx^{10} in \left(1+\mathrmx^{2}\right)^{30}={ }^{30} \mathrm{C}_{5}={ }^{30} \mathrm{C}_{30-5}={ }^{30} \mathrm{C}_{25}

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