Question

Coefficient of x in $(1-2x^{3}3x^5)(1+\frac{1}{x}{)}^8$ is

• A. 123
• B. 154
• C. 95
• D. 136

Answer 1

The correct option is B 154

$(1-2x^3+3x^5)[1+\frac{{}^8{c}_1}{x}+\frac{{}^8{c}_2}{x^2}+\frac{{}^8{c}_3}{x^3}+\cdots \frac{{}^8{c}_7}{x^7}+\frac{{}^8{c}_8}{x^8}]$

$\text{Cofficient of}x=$$-2\left({}^8{c}_2\right)+3\times {}^8{c}_4$

$=\frac{-2\times \cdot 8!}{6!\times 2!}+3\times \frac{8!}{4!\times 4!}$

$=\frac{-2\times 8!}{6!\times 2!}+3\times \frac{8!}{4!\times 4!}$

$=-56+210$

$=154$

$\text{option (b)}$