The coefficient of ${x^{-9}}$ in the expansion of ${\left( \frac{x^2}{2} - \frac{2}{x} \right)^9}$ is

The independent term in the expansion of $(1+x+2x^2)(\frac{3x^2}{2}-\frac{1}{3x})^9$ is

The term independent of $y$ in the expansion of $(y^{-1/6} - y^{1/3})^9$ is

Let $s_1 = \sum_{j=1}^{10} j(j-1) \binom{10}{j}$,$s_2 = \sum_{j=1}^{10} j \binom{10}{j}$,and $s_3 = \sum_{j=1}^{10} j^2 \binom{10}{j}$.
Statement $-1$: $s_3 = 55 \times 2^9$
Statement $-2$: $s_1 = 90 \times 2^8$ and $s_2 = 10 \times 2^8$

The coefficient of ${x^{39}}$ in the expansion of ${\left( {{x^4} - \frac{1}{{{x^3}}}} \right)^{15}}$ is

If the fourth term in the binomial expansion of $\left(\sqrt{\frac{1}{x^{1+\log _{10} x}}}+x^{\frac{1}{12}}\right)^{6}$ is equal to $200$,and $x > 1$,then the value of $x$ is