If (1 + ax)^n = 1 + 8x + 24x^2 + .... then a n is: - Vidyadip

MCQ

If $(1 + ax)^n = 1 + 8x + 24x^2 + ....$ then $a \times n$ is:

✓
$8$
B
$12$
C
$16$
D
$24$

✓

Answer

Correct option: A.

$8$

$(1+a x)^n=1+8 x+24 x^2+\ldots \ldots \ldots $
$\Rightarrow{ }^n C_0+{ }^n C_1(a x)+{ }^n C_2 \cdot(a x)^2+\ldots \ldots=1+8 x+24 a x^2 \ldots \ldots \ldots $
$ \Rightarrow 1+(n a) x+{ }^n C_2 \cdot(a x)^2+\ldots \ldots=1+8 x+24 a x^2 \ldots \ldots \ldots$
Comparing coefficient of $x$ in $\text{R.H.S}$ to that in $\text{L.H.S}$.
Thus $n \times a = 8$

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