Binomial Theorem And Its Simple Applications Question 155
Question: If $ {{(1+ax)}^{n}}=1+8x+24x^{2}+…., $ then the value of a and n is
[IIT 1983; Pb. CET 1994, 99]
Options:
A) 2, 4
B) 2, 3
C) 3, 6
D) 1, 2
Show Answer
Answer:
Correct Answer: A
Solution:
- As given $ {{(1+ax)}^{n}}=1+8x+24x^{2}+…. $
therefore $ 1+\frac{n}{1}ax+\frac{n(n-1)}{1.2}a^{2}x^{2}+….=1+8x+24x^{2}+…. $
$ \Rightarrow na=8,\frac{n(n-1)}{1.2}a^{2}=24\Rightarrow na(n-1)a=48 $
therefore $ 8(8-a)=48 $
therefore $ 8-a=6\Rightarrow a=2\Rightarrow n=4 $ .
BETA
