If the coefficient of the middle term in the expansion of ${(1 + x)^{2n + 2}}$ is $p$ and the coefficients of middle terms in the expansion of ${(1 + x)^{2n + 1}}$ are $q$ and $r$, then
$p + q = r$
$p + r = q$
$p = q + r$
$p + q + r = 0$
The term independent of $x$ in expansion of ${\left( {\frac{{x + 1}}{{{x^{2/3}} - {x^{\frac{1}{3}}} + 1\;}}--\frac{{x - 1}}{{x - {x^{1/2}}}}} \right)^{10}}$ is
The term independent of $x$ in the expansion of ${\left( {{x^2} - \frac{1}{x}} \right)^9}$ is
If the sum of the coefficients in the expansion of $(x - 2y + 3 z)^n,$ $n \in N$ is $128$ then the greatest coefficie nt in the exp ansion of $(1 + x)^n$ is
The coefficient of $\frac{1}{x}$ in the expansion of ${\left( {1 + x} \right)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ is :-