The term independent of $x$ in ${\left( {2x - \frac{1}{{2{x^2}}}} \right)^{12}}$is

If for positive integers $r > 1,n > 2$ the coefficient of the ${(3r)^{th}}$ and ${(r + 2)^{th}}$ powers of $x$ in the expansion of ${(1 + x)^{2n}}$ are equal, then

The number of integral terms in the expansion of ${\left( {\sqrt 3 + \sqrt[8]{5}} \right)^{256}}$ is

If the coefficients of $(r-5)^{th}$ and $(2 r-1)^{th}$ terms in the expansion of $(1+x)^{34}$ are equal, find $r$

If the coefficients of $x^2$ and $x^3$ are both zero, in the expansion of the expression $(1 + ax + bx^2) (1 -3x)^{t5}$ in powers of $x$, then the ordered pair $(a, b)$ is equal to

If the coefficient of $4^{th}$ term in the expansion of ${(a + b)^n}$ is $56$, then $n$ is