Question

The coefficient of $x^6$ in the expansion of ${(1+\frac{x}{\angle 1}+\frac{x^2}{\angle 2}+\frac{x^3}{\angle 3}+\frac{x^4}{\angle 4}+\frac{x^5}{\angle 5})}^2$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Coefficient of $x^6$ is $\frac{1}{\angle 5}\frac{1}{\angle 1}+\frac{1}{\angle 4}\frac{1}{\angle 2}+\frac{1}{\angle 3}\frac{1}{\angle 3}+\frac{1}{\angle 2}\frac{1}{\angle 4}+\frac{1}{\angle 1}\frac{1}{\angle 5}=\frac{1}{\angle 6}{[}^6{C}_1{+}^6{C}_2{+}^6{C}_3{+}^6{C}_4{+}^6{C}_5]=\frac{1}{\angle 6}(2^6-2)=\frac{31}{360}$