Coefficient of x^{18} in expansion of left(x^4-frac{1}{x^3}right)^{15} is ........... .

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7.Binomial Theorem

hard

The coefficient of $x^{18}$ in the expansion of $\left(x^4-\frac{1}{x^3}\right)^{15}$ is $...........$.

A

$5004$

B

$5003$

C

$5002$

D

$5005$

(JEE MAIN-2023)

Solution

$\left(x^4-\frac{1}{x^3}\right)^{15}$

$T_{r+1}={ }^{15} C_r\left(x^4\right)^{15-r}\left(\frac{-1}{x^3}\right)^r$

$60-7 r=18$

$r=6$

Hence coeff. of $x^{18}={ }^{15} C _6=5005$

Standard 11

Mathematics

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