Number of rational terms in the expansion of ${\left( {\sqrt 2 \,\, + \,\,\sqrt[4]{3}} \right)^{100}}$ is :

The term independent of $x$ in ${\left[ {\sqrt{\frac{ x }{3}} + \frac{{\sqrt 3 }}{{{x^2}}}} \right]^{10}}$ is

The number of rational terms in the binomial expansion of $\left(4^{\frac{1}{4}}+5^{\frac{1}{6}}\right)^{120}$ is $....$

The middle term in the expansion of ${(1 + x)^{2n}}$ is

The number of integral terms in the expansion of $(7^{1/3} + 11^{1/9})^{6561}$ is :-

The greatest coefficient in the expansion of ${(1 + x)^{2n + 1}}$ is