Number of integral terms in the expansion of { 7 ( 1 2 ) + 11 ( 1 6 ) } 824 is equal to _______ . [2024]

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.
Number of integral terms in the expansion of ${7^{(\frac{1}{2})} + 11^{(\frac{1}{6})}}^{824}$ is equal to _______ . [2024]

Ans.
(138)

We have, ${7^{(\frac{1}{2})} + 11^{(\frac{1}{6})}}^{824}$

Now, ${(n + 1)}^{th}$ term $= t_{n + 1} = {}^{n}{C_{r}} 11^{\frac{r}{6}} 7^{\frac{824 - r}{2}}$

For integral term, 6 should divide $r$ and $\frac{824 - r}{2}$ must be integer.

$\Rightarrow 2$ must divide $r$ and $r$ is divisible by 6

Possible values of $r$ so that integral terms are obtained i.e., 0, 6, 12, ... 822

Now, this is an A.P. so let $n$ be number of integral terms

$∴$ $822 = 0 + (n - 1) 6 \Rightarrow n = 138$

So, 138 integral terms will be there in the expansion.

Want Us to Email you About Special Offers & Updates?