Coefficient of x12 in (1+x3)5(1+x4)8(1+x5)11 is

Question

Coefficient of x12 in (1+x3)5(1+x4)8(1+x5)11 is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Possible powers of x in (1+x3)5=0,3,6,9,12, ldots(1+x4)8 =0,4,8,12, ldots and in (1+x5)11=0,5,10, ldots Possibilities for x12 is <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a32a1c0d1428132a124a0ad688391f99-.png" /> ⇒ 501

Q. Coefficient of $x^{12}$ in $(1 + x^{3})^{5} (1 + x^{4})^{8} (1 + x^{5})^{11}$ is

Possible powers of $x$
in $(1 + x^{3})^{5} = 0, 3, 6, 9, 12, \dots (1 + x^{4})^{8}$
$= 0, 4, 8, 12, \dots$ and in $(1 + x^{5})^{11} = 0, 5, 10, \dots$
Possibilities for $x^{12}$ is

$\Rightarrow 501$

Q. Coefficient of x12 in (1+x3)5(1+x4)8(1+x5)11 is

Possible powers of x in (1+x3)5=0,3,6,9,12,…(1+x4)8 =0,4,8,12,… and in (1+x5)11=0,5,10,… Possibilities for x12 is ⇒501

Q. Coefficient of $x^{12}$ in $(1 + x^{3})^{5} (1 + x^{4})^{8} (1 + x^{5})^{11}$ is

Possible powers of $x$
in $(1 + x^{3})^{5} = 0, 3, 6, 9, 12, \dots (1 + x^{4})^{8}$
$= 0, 4, 8, 12, \dots$ and in $(1 + x^{5})^{11} = 0, 5, 10, \dots$
Possibilities for $x^{12}$ is

$\Rightarrow 501$