The coefficient of $x^{4}$ is the expansion of $\left(1+\mathrm{x}+\mathrm{x}^{2}\right)^{10}$ is

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

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

The sum of the binomial coefficients of ${\left[ {2\,x\,\, + \,\,\frac{1}{x}} \right]^n}$ is equal to $256$ . The constant term in the expansion is

The number of integral terms in the expansion of $\left(3^{\frac{1}{2}}+5^{\frac{1}{4}}\right)^{680}$ is equal to