Question

If ${(1+ax)}^n=1+8x+24x^2+......,$ then the value of a and n is

• A. 2, 4
• B. 2, 3
• C. 3,6
• D. 1,2

Answer 1

The correct option is A 2, 4

As given ${(1+ax)}^n=1+8x+24x^2+......,$
$\Rightarrow 1+\frac{n}{1}ax+\frac{n(n-1)}{1.2}{a}^2{x}^2+....=1+8x+24x^2+....$
$\Rightarrow na=8,\frac{n(n-1)}{1.2}{a}^2=24\Rightarrow na(n-1)a=48$
$\Rightarrow 8(8-a)=48\Rightarrow 8-a=6\Rightarrow a=2\Rightarrow n=4$