In the expansion of ${\left( {2{x^2} - \frac{1}{x}} \right)^{12}}$, the term independent of x is

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

For the natural numbers $m, n$, if $(1-y)^{m}(1+y)^{n}=1+a_{1} y+a_{2} y^{2}+\ldots .+a_{m+n} y^{m+n}$ and $a_{1}=a_{2}$ $=10$, then the value of $(m+n)$ is equal to:

Find the $13^{\text {th }}$ term in the expansion of $\left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}, x \neq 0$

Arrange the expansion of $\left(x^{1 / 2}+\frac{1}{2 x^{1 / 4}}\right)^n$ in decreasing powers of $x$.Suppose the coeff icients of the first three terms form an arithmetic progression. Then, the number of terms in the expansion having integer power of $x$ is

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