First slide

Binomial theorem for positive integral Index

Question

Let $a_{r}$ denote the coefficient of $y^{r - 1}$ in the expansion of ${(1 + 2 y)}^{10}$ . If $\frac{a_{r + 2}}{a_{r}} = 4$ , then $r$ is equal to

Moderate

A

2
B

3
C

4
D

5

Solution

$T_{r + 1} =^{10} C_{r} (2 y)^{r} = (^{10} C_{r} 2^{r}) y^{r} .$
$∴ a_{r} =^{10} C_{r} 2^{r}$
Now
$\begin{aligned} 4 = \frac{a_{r + 2}}{a_{r}} = \frac{^{10} C_{r + 2}}{^{10} C_{r}} \frac{2^{r + 2}}{2^{r}} \\ \Rightarrow^{10} C_{r + 2} =^{10} C_{r} \Rightarrow r + 2 = 10 - r \Rightarrow r = 4 \end{aligned}$

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