The total number of irrational terms in the binomial expansion of $(7^{1/5} - 3^{1/10})^{60}$ is:

The term independent of $x$ in the expansion of $\left( \frac{1}{60} - \frac{x^8}{81} \right) \left( 2x^2 - \frac{3}{x^2} \right)^6$ is equal to

If the coefficient of the middle term in the expansion of $(1 + x)^{2n + 2}$ is $p$ and the coefficients of the two middle terms in the expansion of $(1 + x)^{2n + 1}$ are $q$ and $r$,then:

If the constant term in the binomial expansion of $\left(\frac{x^{5/2}}{2} - \frac{4}{x^{\ell}}\right)^9$ is $-84$ and the coefficient of $x^{-3\ell}$ is $2^{\alpha}\beta$,where $\beta < 0$ is an odd number,then $|\alpha\ell - \beta|$ is equal to

If the ratio of the terms equidistant from the middle term in the expansion of $(1+x)^{12}$ is $\frac{1}{256}$ $(x \in N)$,then the sum of all the terms of the expansion $(1+x)^{12}$ is:

The coefficient of ${x^2}$ in the expansion of ${\left( x - \frac{1}{2x} \right)^8}$ is