The coefficient of the term independent of $x$ in the expansion of ${\left( {\sqrt {\frac{x}{3}} + \frac{3}{{2{x^2}}}} \right)^{10}}$ is
$5/4$
$7/4$
$9/4$
none of these
If $\frac{{{T_2}}}{{{T_3}}}$ in the expansion of ${(a + b)^n}$ and $\frac{{{T_3}}}{{{T_4}}}$ in the expansion of ${(a + b)^{n + 3}}$ are equal, then $n=$
The sum of the real values of $x$ for which the middle term in the binomial expansion of ${\left( {\frac{{{x^3}}}{3} + \frac{3}{x}} \right)^8}$ equals $5670$ is
Find the expansion of $\left(3 x^{2}-2 a x+3 a^{2}\right)^{3}$ using binomial theorem
The positive value of $\lambda $ for which the co-efficient of $x^2$ in the expression ${x^2}{\left( {\sqrt x + \frac{\lambda }{{{x^2}}}} \right)^{10}}$ is $720$ is
If the coefficients of $x^4, x^5$ and $x^6$ in the expansion of $(1+x)^n$ are in the arithmetic progression, then the maximum value of $n$ is :