In the expansion of (1 + 3x + 2x2)6, the coefficient of x11 is

Question

In the expansion of (1 + 3x + 2x2)6, the coefficient of x11 is (A) 144 (B) 288 (C) 216 (D) 576

Tardigrade Admin · Accepted Answer

(1 + 3x + 2x2)6 = ((1 +3x) + (2x2))6 = 6C0(1+3x)6 + 6C1(1 + 3x)5 2x2 + 6C2(1 + 3x)4(2x2)2 + 6C3(1 + 3x)3(2x2)3 + 6C4(1 + 3x)2(2x2)4 + 6C5(1 + 3x) × (2x2)5 + 6C6(2x2)6 ∴ Coefficient of x11 in above expression = 6C5⋅ 3⋅ 32 = 6 × 3 × 32 = 576

Q. In the expansion of $(1 + 3 x + 2 x^{2})^{6}$ , the coefficient of $x^{11}$ is

$144$

$288$

$216$

$576$

Q. In the expansion of (1+3x+2x2)6, the coefficient of x11 is

144

288

216

576

(1+3x+2x2)6=((1+3x)+(2x2))6 =6C0​(1+3x)6+6C1​(1+3x)52x2+6C2​(1+3x)4(2x2)2 +6C3​(1+3x)3(2x2)3+6C4​(1+3x)2(2x2)4+6C5​(1+3x)× (2x2)5+6C6​(2x2)6 ∴ Coefficient of x11 in above expression =6C5​⋅3⋅32 =6×3×32=576

Q. In the expansion of $(1 + 3 x + 2 x^{2})^{6}$ , the coefficient of $x^{11}$ is

$144$

$288$

$216$

$576$