The coefficient of x 18 in the expansion of ( x 4 - 1 x 3 ) 15 is __________ . [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
The coefficient of $x^{18}$ in the expansion of ${(x^{4} - \frac{1}{x^{3}})}^{15}$ is __________ . [2023]

Ans.
(5005)

Given, ${(x^{4} - \frac{1}{x^{3}})}^{15}$

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

$= {}^{15}{C_{r}} {(x)}^{60 - 4 r} \cdot {(- 1)}^{r} x^{- 3 r} = {}^{15}{C_{r}} {(x)}^{60 - 7 r} \cdot {(- 1)}^{r}$

For the coefficient of $x^{18}$

$60 - 7 r = 18 \Rightarrow r = \frac{42}{7} = 6$

Hence, coefficient of $x^{18}$ is ${}^{15}{C_{6}} {(- 1)}^{6} = 5005$

Want Us to Email you About Special Offers & Updates?