The number of terms in the expansion of ${\left( {\sqrt[4]{9} + \sqrt[6]{8}} \right)^{500}}$, which are integers is
$501$
$251$
$42$
$41$
In the expansion of $(1 + x + y + z)^4$ the ratio of coefficient of $x^2y, xy^2z, xyz$ are
Find the coefficient of $a^{4}$ in the product $(1+2 a)^{4}(2-a)^{5}$ using binomial theorem.
In the expansion of ${\left( {x - \frac{3}{{{x^2}}}} \right)^9},$ the term independent of $x$ is
The term independent of ' $x$ ' in the expansion of $\left(\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right)^{10}$, where $x \neq 0,1$ is equal to $.....$
If coefficient of ${(2r + 3)^{th}}$ and ${(r - 1)^{th}}$ terms in the expansion of ${(1 + x)^{15}}$ are equal, then value of r is