Given that $4^{th}$ term in the expansion of ${\left( {2 + \frac{3}{8}x} \right)^{10}}$ has the maximum numerical value, the range of value of $x$ for which this will be true is given by
$ - \frac{{64}}{{21}} < x < - 2$
$ - \frac{{64}}{{21}} < x < 2$
$\frac{{64}}{{21}} < x < 4$
None of these
The term independent of $x$ in ${\left( {2x - \frac{1}{{2{x^2}}}} \right)^{12}}$is
The coefficient of $x^2$ in the expansion of the product $(2 -x^2)$. $((1 + 2x + 3x^2)^6 +(1 -4x^2)^6)$ is
If the $6^{th}$ term in the expansion of the binomial ${\left[ {\frac{1}{{{x^{\frac{8}{3}}}}}\,\, + \,\,{x^2}\,{{\log }_{10}}\,x} \right]^8}$ is $5600$, then $x$ equals to
The coefficient of ${x^5}$ in the expansion of ${(x + 3)^6}$ is
In the expansion of ${\left( {{x^2} - 2x} \right)^{10}}$, the coefficient of ${x^{16}}$ is