The term independent of $x$ in the binomial expansion of $\left( {1 - \frac{1}{x} + 3{x^5}} \right){\left( {2{x^2} - \frac{1}{x}} \right)^8}$ is

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

If the second, third and fourth terms in the expansion of $(x+y)^{\mathrm{n}}$ are $135$,$30$ and $\frac{10}{3}$, respectively, then $6\left(n^3+x^2+y\right)$ is equal to .............

In the expansion of $(1 + x + y + z)^4$ the ratio of coefficient of $x^2y, xy^2z, xyz$ are

If the coefficients of $x^7$ in $\left( ax ^2+\frac{1}{2 bx }\right)^{11}$ and $x ^{-7}$ in $\left(a x-\frac{1}{3 b x^2}\right)^{11}$ are equal, then

The coefficient of $x^{13}$ in the expansion of $(1 -x)^5(1 + x + x^2 + x^3)^4$ is :-