If the coefficients of x and x 2 in ( 1 + x ) p ( 1 - x ) q are 4 and - 5 respectively, then 2 p + 3 q 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 coefficients of $x$ and $x^{2}$ in ${(1 + x)}^{p} {(1 - x)}^{q}$ are 4 and $- 5$ respectively, then $2 p + 3 q$ is equal to [2023]

1 66

2 60

3 63

4 69

Ans.
(3)

${(1 + x)}^{p} {(1 - x)}^{q} = [1 + p x + \frac{p (p - 1)}{2} x^{2} + \dots] [1 - q x + \frac{q (q - 1)}{2} x^{2} + \dots]$

$∴$ $Coefficient of x = p - q = 4 ...(i)$

Coefficient of $x^{2}$ = $\frac{q (q - 1)}{2} - p q + \frac{p (p - 1)}{2} = - 5$

$\Rightarrow {(p - q)}^{2} - (p + q) = - 10 \Rightarrow p + q = 26 ...(ii)$

So, from (i) and (ii),

$p = 15, q = 11$ $∴$ $2 p + 3 q = 30 + 33 = 63$

Want Us to Email you About Special Offers & Updates?