Coefficient of $t^{20}$ in the expansion of $(1 + t^2)^{10}(1 + t^{10})(1 + t^{20})$ is

The term independent of $x$ in the expansion of $\left( {\frac{1}{{60}} – \frac{{{x^8}}}{{81}}} \right).{\left( {2{x^2} – \frac{3}{{{x^2}}}} \right)^6}$ is equal to

If the middle term in the expansion of ${\left( {{x^2} + \frac{1}{x}} \right)^n}$ is $924{x^6}$, then $n = $

The sum of all rational terms in the expansion of $\left(2^{\frac{1}{5}}+5^{\frac{1}{3}}\right)^{15}$ is equal to :

The sum of the real values of $x$ for which the middle term in the binomial expansion of ${\left( {\frac{{{x^3}}}{3} + \frac{3}{x}} \right)^8}$ equals $5670$ is