Question

If the sum of the coefficients in the expansion of ${(x-2y+3z)}^n$ is 128, then the greatest coefficient in the expansion of ${(1+x)}^n$ is....

• A. 35
• B. 20
• C. 10
• D. None of these

Answer 1

Answer: (A)

35

Sum of the coefficients in the expansion ${\left(x-2y+3z\right)}^n={\left(1-2+3\right)}^n=128$

${\left(2\right)}^n=2^7$

$n=7$

$\therefore$ greatest coefficient in the expansion

${\left(1+x\right)}^7{=}^7{c}_3$

$=\frac{7!}{3!4!}=\frac{7\times 6\times 5}{6}=35$

Hence,

option $\left(A\right)$ is correct answer.