Coefficient of {x^{32}} in expansion of {left( {{x^4} - frac{1}{{{x^3}}}} right)^{15}} is

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7.Binomial Theorem

easy

The coefficient of ${x^{32}}$ in the expansion of ${\left( {{x^4} - \frac{1}{{{x^3}}}} \right)^{15}}$ is

A

$^{15}{C_5}$

B

$^{15}{C_6}$

C

$^{15}{C_4}$

D

$^{15}{C_7}$

Solution

(c) Let ${T_{r + 1}}$ term containing $x^{32}$

$\therefore ^{15}{C_r}{x^{4r}}{\left( {\frac{{ – 1}}{{{x^3}}}} \right)^{15 – r}}$

==> ${x^{4r}}{x^{ – 45 + 3r}} = {x^{32}}$

$\Rightarrow 7r = 77 $

$\Rightarrow r = 11$.

Hence coefficient of $x^{32}$ is $^{15}{C_{11}}$ or $^{15}{C_4}$

Standard 11

Mathematics

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