The middle term in the expansion of ${(1 + x)^{2n}}$ is
$\frac{{(2n)!}}{{n!}}{x^2}$
$\frac{{(2n)!}}{{n!(n - 1)!}}{x^{n + 1}}$
$\frac{{(2n)!}}{{{{(n!)}^2}}}{x^n}$
$\frac{{(2n)!}}{{(n + 1)!(n - 1)!}}\,{x^n}$
In the expansion of $(1 + x + y + z)^4$ the ratio of coefficient of $x^2y, xy^2z, xyz$ are
Middle term in the expansion of ${(1 + 3x + 3{x^2} + {x^3})^6}$ is
The term independent of $x$ in the expansion of ${\left( {2x - \frac{3}{x}} \right)^6}$ is
Find the coefficient of $x^{5}$ in the product $(1+2 x)^{6}(1-x)^{7}$ using binomial theorem.
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