Binomial Theorem question bank (Maths)

If $26\left(\dfrac{2^3}{3}\binom{12}{2} + \dfrac{2^5}{5}\binom{12}{4} + \dfrac{2^7}{7}\binom{12}{6} + \ldots + \dfrac{2^{13}}{13}\binom{12}{12}\right) = 3^{13} - \alpha$, then $\alpha$ is equal to:

If $(1 - x^3)^{10} = \sum\limits_{r=0}^{10} a_r x^r (1-x)^{30-2r}$, then $\dfrac{9a_9}{a_{10}}$ is equal to __________.