Question

If $(1+ax{)}^n$ = 1 + 8x + 24 $x^2$ + ......, 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 + 24$x^2$ + .........

⇒ 1 + $\frac{n}{1}$ax + $\frac{n(n-1)}{1.2}$$a^2{x}^2$ + ......... = 1 + 8x + 24$x^2$ + ...........

⇒na = 8, $\frac{n(n-1)}{1.2}$$a^2$ = 24 ⇒ na(n-1)a = 48

⇒8(8 - a) = 48 ⇒ 8 - a = 6 ⇒ a = 2 ⇒ n = 4.