First slide

Binomial theorem for positive integral Index

Question

If the sum of the coefficients in the expansion of ${(x + y)}^{n}$ is 2048, then the greatest coefficient in the expansion is :

Moderate

A

$^{10} C_{6}$
B

$^{11} C_{6}$
C

$^{11} C_{7}$
D

$^{12} C_{6}$

Solution

Sum of the coefficients in the expansion of $(x + y)^{n}$ is $2^{n}$ . Therefore,
$2^{n} = 2048 = 2^{11} \Rightarrow n = 11$
As $n$ is odd, the greatest value of $^{n} C_{r} {is}^{n} C_{k}$ where
$k = \frac{1}{2} (n - 1) or k = \frac{1}{2} (n + 1)$
Here $n = 11$ , therefore $k = 5$ or $6$
Thus, greatest coefficient is $^{11} C_{6}$ .

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App