If 1-a xn-1-8 x-24 x2- then the value of a and n isA- 3-6B- 1-2C- 2-4D- 2-3

The correct option is C 2, 4 As given (1 + ax)^n = 1 + 8x + 24x^2 + ......... ⇒ 1 + n/1ax + n(n 1)/1.2a^2x^2 + ......... = 1 + 8x + 24x^2 + ........... ⇒na = ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Binomial Theorem

If 1+a xn=1+8...

Question

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

and n is

2, 4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2, 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3, 6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1, 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
2, 4

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.

Suggest Corrections

Similar questions

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

Q. If

{(1 + a x)}^{n} = 1 + 8 x + 24 x^{2} + . . . . . .,

then the value of a and n is

Q. If

(1 + a x)^{n} = 1 + 8 x + 24 x^{2} + . . . .

then

a \times n

is:

Q. If

(1 + a x)^{n} = 1 + 8 x + 24 x^{2} + . . .;

then

\frac{a - n}{a + n}

is equal to

Q. If

(1 + a x)^{n} = 1 + 8 x + 24 x^{2} + . . .,

then which of the following is/are correct?

Join BYJU'S Learning Program

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

The correct option is A 2, 4 As given (1+ax)n = 1 + 8x + 24x2 + ......... ⇒ 1 + n1ax + n(n−1)1.2a2x2 + ......... = 1 + 8x + 24x2 + ........... ⇒na = 8, n(n−1)1.2a2 = 24 ⇒ na(n-1)a = 48 ⇒8(8 - a) = 48 ⇒ 8 - a = 6 ⇒ a = 2 ⇒ n = 4.

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

and n is