Answer:
Option C
Explanation:
Plan Coefficient of xr in (1+x)n is nCr
In this type of questions, we find differemnt composition of terms where product will give us x11
Coefficient of x11 in $(1+x^{2})^{4}(1+x^{3})^{7}(1+x^{4})^{12}$
Now,consider the following cases for x11 in $(1+x^{2})^{4}(1+x^{3})^{7}(1+x^{4})^{12}$
Coefficient of x0 x3 x8 : coefficient of x2 x9 x0
Coefficient of x4 x3 x4 : coefficient of x8 x3 x0
= $^{4}C_{0}\times^{7}C_{1}\times^{12}C_{2}+^{4}C_{1}\times^{7}C_{3}\times^{12}C_{0}+$
$^{4}C_{2}\times^{7}C_{1}\times^{12}C_{2}+^{4}C_{4}\times^{7}C_{1}\times^{12}C_{0}$
= 462+140+504+7=1113
