Number of rational terms in the expansion of ${\left( {{3^{\frac{1}{8}}} + {5^{\frac{1}{3}}}} \right)^{400}}$ is

In the expansion of ${\left( {\frac{{x\,\, + \,\,1}}{{{x^{\frac{2}{3}}}\,\, - \,\,{x^{\frac{1}{3}}}\,\, + \,\,1}}\,\, - \,\,\frac{{x\,\, - \,\,1}}{{x\,\, - \,\,{x^{\frac{1}{2}}}}}} \right)^{10}}$, the term which does not contain $x$ is :

If the constant term in the expansion of $\left(1+2 x-3 x^3\right)\left(\frac{3}{2} x^2-\frac{1}{3 x}\right)^9$ is $p$, then $108$ p is equal to....................

If in the expansion of ${(1 + x)^{21}}$, the coefficients of ${x^r}$ and ${x^{r + 1}}$ be equal, then $r$ is equal to

In the expansion of ${(1 + 3x + 2{x^2})^6}$ the coefficient of ${x^{11}}$ is

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