Question

The coefficient of $x^{4}$ in the expansion of $\left(1 + 5 x + 9 x^{2} + 13 x^{3} + 17 x^{4} + . \ldots \ldots \right)\left(1 + x^{2}\right)^{11}$ is equal to

• A. $^{11}C_{2}+4^{11}C_{1}+3$
• B. $^{11}C_{2}+3^{11}C_{1}+4$
• C. $3^{11}C_{2}+4^{11}C_{1}+3$
• D. $171$

Answer 1

Answer: (D)

Coefficient of $x^{4}$ in $\left(1+5 x+9 x^{2}+13 x^{3}+17 x^{4}+\ldots \ldots .\right)\left(1+11 x^{2}+{ }^{11} C_{2} x^{4}+\ldots \ldots\right)$
Coefficient of $x^{4}$ is $={ }^{11} C_{2}+9 \times 11+17 \times 1$
$=\frac{11 \times 10}{2}+99+17$
$=55+99+17$
$=171$