Question

The co-efficient of x in the expansion of $(1-2x^3+3x^5){(1+\frac{1}{x})}^8$ is :

• A. 56
• B. 65
• C. 154
• D. 62

Answer 1

The correct option is C 154

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

$(1-2x^3+3x^5){(}^8{C}_0{+}^8{C}_1\frac{1}{x}{+}^8{C}_2{+}^8{C}_3\frac{1}{x^3}+..{.}^8{C}_4)$

$={3.}^8{C}_4-2^8{C}_2$

$=\frac{3.8!}{4.4!}-2\times \frac{8!}{6!2!}$

$=\frac{3\times 8\times 7\times 6\times 5\times 4!}{4\times 3\times 2\times 4!}-\frac{2\times 8\times 7\times 6!}{6!\times 2!}$

$=210-56$

$=154$