The coefficient of x 18 in the expansion of x 4 - 1 x 3 15 is _ _ _ _ _ _ _ _ _ _ _ _

Given, Binomial expression x 4 - 1 x 3 15 Now general term is given by, T r + 1 = C r 15 x 4 15 - r - 1 x 3 r ⇒ T r + 1 = C r 15 x 60 - 7 r ( - 1 ) r For coefficient of x 18 , equate 60 - 7 r = 18 ⇒ r = 6 Coefficient of x 18 = - 1 6 · C 6 15 = 5005

Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremGeneralEasy2 minPYQ_2023

MathematicsEasynumerical

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

Answer:

5005.00

Solution:

Given,
Binomial expression ${(x^{4} - \frac{1}{x^{3}})}^{15}$
Now general term is given by,
$T_{r + 1} = {}^{15}C_{r} {(x^{4})}^{15 - r} {(- \frac{1}{x^{3}})}^{r}$
$\Rightarrow T_{r + 1} = {}^{15}C_{r} x^{60 - 7 r} (- 1)^{r}$
For coefficient of $x^{18},$ equate $60 - 7 r = 18$
$\Rightarrow r = 6$
Coefficient of $x^{18} = {(- 1)}^{6} \cdot {}^{15}C_{6} = 5005$

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:General

⏱ 2mℹ️ Source: PYQ_2023

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