Explanation

(a)
∵ 10th term in the expansion of ${(2 - 3x}^{3})^{20}$ is $\ ^{20}C_{9}2^{9}( - 1)^{9}(2)^{11}(3)^{9}x^{27}$ and 11th term is $\ ^{20}C_{10}2^{10}3^{10}x^{30}$
$\therefore\ \ \ \ \ \frac{\ ^{20}C_{9}( - 1)^{9}(2)^{11}(3)^{9}x^{27}}{\ ^{20}C_{10} \bullet 2^{10} \bullet 3^{10} \bullet x^{30}} = \frac{45}{22}$
$\Longrightarrow \ \ \ \ \ - \frac{10}{11} \bullet \frac{2}{{3x}^{3}} = \frac{45}{22}$
$\Longrightarrow \ \ \ \ x^{3} = - \frac{8}{27} \Longrightarrow x = - \frac{2}{3}$