Question

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

• A. $8$
• B. $12$
• C. $16$
• D. $24$

Answer 1

Answer: (A)

$8$

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

$\Rightarrow$${}^n{C}_0{+}^n{C}_1\left(ax\right){+}^n{C}_2.{\left(ax\right)}^2+......=1+8x+24a{x}^2..........$

$\Rightarrow$$1+\left(na\right)x{+}^n{C}_2.{\left(ax\right)}^2+......=1+8x+24a{x}^2..........$

Comparing coefficient of $x$ in R.H.S to that in L.H.S.

Thus $n\times a=8$