If the non zero coefficient of $(2r + 4)th$ term is greater than non zero coefficient of $(r - 2)th$ term in expansion of $(1 + x)^{18}$, then number of possible integral values of $r$ is

Expand using Binomial Theorem $\left(1+\frac{ x }{2}-\frac{2}{ x }\right)^{4}, x \neq 0$

The coefficient of $x^4$ in ${\left[ {\frac{x}{2}\,\, - \,\,\frac{3}{{{x^2}}}} \right]^{10}}$ is :

The number of terms in the expansion of  ${\left( {\sqrt[4]{9} + \sqrt[6]{8}} \right)^{500}}$, which are integers is

Find the term independent of $x$ in the expansion of $\left(\sqrt[3]{x}+\frac{1}{2 \sqrt[3]{x}}\right)^{18}, x\,>\,0$

If the $1011^{\text {th }}$ term from the end in the binomial expansion of $\left(\frac{4 x}{5}-\frac{5}{2 x }\right)^{2022}$ is $1024$ times $1011^{\text {th }}$ term from the beginning, then $|x|$ is equal to