Q. The coefficient of $x^{20}$ in the expansion of $(1 + 3x + 3x^{2} + x^{3})^{20}$ is
A) $\ ^{60}C_{40}\ \$
B) $\ ^{30}C_{20}\ \$
C) $\ ^{15}C_{2}\ \$
D) None of these
Explanation
(a)
$({1 + 3x + {3x}^{2} + x^{3})}^{20} = (1 + x)^{60}$
$\therefore$ Coefficent of $x^{20}$in ${(1 + x)}^{60}is\ \ ^{60}C_{20}or\ \ \ ^{60}C_{40}.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.