First slide

Binomial theorem for positive integral Index

Question

If $(1 + ax)^{n} = 1 + 8 x + 24 x^{2} + \dots, t$ then the values of $a$ and $n$ are

Moderate

A

2,4
B

2,3
C

3,6
D

1,2

Solution

Given that, $(1 + ax)^{n} = 1 + 8 x + 24 x^{2} + \dots$
$1 + \frac{n}{1} ax + \frac{n (n - 1)}{1 \cdot 2} a^{2} x^{2} + \dots = 1 + 8 x + 24 x^{2} + \dots$
On comparing the coefficients of $x, x^{2}$ we get
$na = 8, \frac{n (n - 1)}{1 \cdot 2} a^{2} = 24$
$\begin{array}{lr} \Rightarrow na (n - 1) a = 48 \\ \Rightarrow 8 (8 - a) = 48 \\ \Rightarrow 8 - a = 6 \Rightarrow a = 2 \\ \Rightarrow n = 4 \end{array}$

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