If the term without x in the expansion of ( x 2 3 x 3 ) 22 is 7315, then is equal to ________ . [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.
If the term without $x$ in the expansion of ${(x^{\frac{2}{3}} + \frac{α}{x^{3}})}^{22}$ is 7315, then $| α |$ is equal to ________ . [2023]

Ans.
(1)

$T_{r + 1} = {}^{22}C_{r} {(x^{\frac{2}{3}})}^{22 - r} \cdot {(\frac{α}{x^{3}})}^{r}$

$= {}^{22}C_{r} \cdot (x^{\frac{44}{3} - \frac{2 r}{3} - 3 r}) \cdot (α^{r})$

For the term without $' x';$ $\frac{44}{3} - \frac{2 r}{3} - 3 r = 0 \Rightarrow \frac{44}{3} = \frac{11 r}{3}$

$∴$ $r = 4$

So, the term without $x$ is ${}^{22}C_{4} α^{4} = 7315$

$\Rightarrow \frac{22 \times 21 \times 20 \times 19}{24} \cdot α^{4} = 7315$

$∴$ $| α |$ $= 1$

Want Us to Email you About Special Offers & Updates?