If ( 1 + a x ) n = 1 + 8x + 24 x 2 + ......, then the value of a and n is Options: A . &nbsp 2, 4 B . &nbsp 2, 3 C . &nbsp 3, 6 D . &nbsp 1, 2

Answer: Option A : A As given ( 1 + a x ) n = 1 + 8x + 24 x 2 + ......... ⇒ 1 + n 1 ax + n ( n − 1 ) 1.2 a 2 x 2 + ......... = 1 + 8x + 24 x 2 + ........... ⇒na = 8, n ( n − 1 ) 1.2 a 2 = 24 ⇒ na(n-1)a = 48 ⇒8(8 - a) = 48 ⇒ 8 - a = 6 ⇒ a = 2 ⇒ n = 4.

If (1+ax)n = 1 + 8x + 24 x2 + ......, then the value of a and n is

Discussion Forum : Binomial Theorem

Question -

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

Options:

A . 2, 4

B . 2, 3

C . 3, 6

D . 1, 2

Answer: Option A
:
A

As given $(1 + a x)^{n}$ = 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.

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