If in the expansion of ${(1 + x)^m}{(1 - x)^n}$, the coefficient of $x$ and ${x^2}$ are $3$ and $-6$ respectively, then m is
$6$
$9$
$12$
$24$
In the expansion of ${\left( {x - \frac{1}{x}} \right)^6}$, the constant term is
If the middle term in the expansion of ${\left( {{x^2} + \frac{1}{x}} \right)^n}$ is $924{x^6}$, then $n = $
The coefficient of ${x^{ - 9}}$ in the expansion of ${\left( {\frac{{{x^2}}}{2} - \frac{2}{x}} \right)^9}$ is
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
If the coefficients of ${p^{th}}$, ${(p + 1)^{th}}$ and ${(p + 2)^{th}}$ terms in the expansion of ${(1 + x)^n}$ are in $A.P.$, then