The smallest natural number $n,$ such that the coefficient of $x$ in the expansion of ${\left( {{x^2}\, + \,\frac{1}{{{x^3}}}} \right)^n}$ is $^n{C_{23}}$ is
$38$
$58$
$23$
$35$
The expression $[x + (x^3-1)^{1/2}]^5 + [x - (x^3-1)^{1/2}]^5$ is a polynomial of degree :
Find the middle terms in the expansions of $\left(3-\frac{x^{3}}{6}\right)^{7}$
The largest term in the expansion of ${(3 + 2x)^{50}}$ where $x = \frac{1}{5}$ is
In the expansion of ${\left( {x - \frac{3}{{{x^2}}}} \right)^9},$ the term independent of $x$ is
If in the expansion of ${(1 + x)^{21}}$, the coefficients of ${x^r}$ and ${x^{r + 1}}$ be equal, then $r$ is equal to