The coefficient of x 20 in the expansion of ( 1 + x 2 ) 40 ⋅ ( x 2 + 2 + x 2 1 ) − 5 is

Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremMiscellaneous/MixedEasy2 minPYQ_2012

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The coefficient of $x^{20}$ in the expansion of $(1 + x^{2})^{40} \cdot (x^{2} + 2 + \frac{1}{x ^{2}})^{- 5}$ is

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Expression $= (1 + x^{2})^{40} \cdot (x + \frac{1}{x})^{- 10}$ $= (1 + x^{2})^{30} \cdot x^{10}$ The coefficient of $x^{20}$ in $x^{10} (1 + x^{2})^{30}$ $=$ the coefficient of $x^{10}$ in $(1 + x^{2})^{30}$ $=^{30} C_{5} =^{30} C_{30 - 5} =^{30} C_{25}$

Stream:BITSATSubject:MathematicsTopic:Binomial TheoremSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: PYQ_2012

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