Question

The coefficient of $6$in expansion of $(1 + x)^{14}$ is.

• A. $9a^{2}$
• B. $10a^{3}$
• C. $10a^{2}$
• D. $10a$

Answer 1

Answer: (B)

$10a^{3}$

Answer 2

Coefficient of $(C_{0} + C_{1} + .... + C_{n})^{2}$ in expansion of $C_{0}^{2} + C_{1}^{2} + ..... + C_{n}^{2}$ $t^{24}$

ie., coefficient of $(1 + t^{2})^{12}(1 + t^{12})(1 + t^{24})$ in expansion of $12C_{6} + 2$

coefficient of $12C_{5}$ in expansion of $12C_{6}$

Now, $12C_{7}$

$x^{5}$ = $(x^{2} - x - 2)^{5}$.