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Model Paper 4 — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsModel Paper 43 Marks
Question
Expand the given expression $\left(\frac{2}{x}-\frac{\pi}{2}\right)^5$
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Answer

Using binomial theorem for the expansion of $\left(\frac{2}{x}-\frac{x}{2}\right)^5$ we have
$\left(\frac{2}{x}-\frac{x}{2}\right)^5={ }^5 C_0\left(\frac{2}{x}\right)^5+{ }^5 C_1\left(\frac{2}{x}\right)^4\left(\frac{-x}{2}\right)+{ }^5 C_2\left(\frac{2}{x}\right)^3\left(\frac{-x}{2}\right)^2+{ }^5 C_3\left(\frac{2}{x}\right)^2\left(\frac{-x}{2}\right)^3 +{ }^5 C_4\left(\frac{2}{x}\right)\left(\frac{-x}{2}\right)^4+{ }^5 C_5\left(\frac{-x}{2}\right)^5$
$=\frac{32}{x^5}+5 \cdot \frac{16}{x^4} \cdot \frac{-x}{2}+10 \cdot \frac{8}{x^3} \cdot \frac{x^2}{4}+10 \cdot \frac{4}{x^2} \cdot \frac{-x^3}{8}+5 \cdot \frac{2}{x} \cdot \frac{x^4}{16}+\frac{-x^5}{32}$
$=\frac{32}{x^5}-\frac{40}{x^3}+\frac{20}{x}-5 x+\frac{5}{8} x^3-\frac{x^5}{32}$

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