If $n$ is even positive integer, then the condition that the greatest term in the expansion of ${(1 + x)^n}$ may have the greatest coefficient also, is
$\frac{n}{{n + 2}} < x < \frac{{n + 2}}{n}$
$\frac{{n + 1}}{n} < x < \frac{n}{{n + 1}}$
$\frac{n}{{n + 4}} < x < \frac{{n + 4}}{4}$
None of these
Find the $13^{\text {th }}$ term in the expansion of $\left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}, x \neq 0$
The term independent of $x$ in the expansion of $\left( {\frac{1}{{60}} - \frac{{{x^8}}}{{81}}} \right).{\left( {2{x^2} - \frac{3}{{{x^2}}}} \right)^6}$ is equal to
In the expansion of ${\left( {{x^2} - 2x} \right)^{10}}$, the coefficient of ${x^{16}}$ is
The term independent of $x$ in the binomial expansion of $\left( {1 - \frac{1}{x} + 3{x^5}} \right){\left( {2{x^2} - \frac{1}{x}} \right)^8}$ is
If the coefficients of the three consecutive terms in the expansion of $(1+ x )^{ n }$ are in the ratio $1: 5: 20$, then the coefficient of the fourth term is $............$.