The coefficients of x7 and x8 in the expansion of (2+x3)n are equal, then n is equal to

Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

The coefficients of $x^{7} and x^{8}$ in the expansion of ${(2 + \frac{x}{3})}^{n}$ are equal, then n is equal to

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Coefficient of $x^{7} = coefficient of x^{8}$

$\Rightarrow^{n} C_{7} 2^{n - 7} . 3^{- 7} =^{n} C_{8} 2^{n - 8} . 3^{- 8}$

$\Rightarrow \frac{^{n} C_{8}}{^{n} C_{7}} = 2 .3$

$\Rightarrow \frac{n - 7}{8} = 6$

$\Rightarrow n - 7 = 48$

$\Rightarrow n = 55$

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE