The absolute difference of the coefficients of $x^{10}$ and $x^7$ in the expansion of $\left(2 x^2+\frac{1}{2 x}\right)^{11}$ is equal to
$12^3-12$
$11^3-11$
$10^3-10$
$13^3-13$
If the coefficient of ${(2r + 4)^{th}}$ and ${(r - 2)^{th}}$ terms in the expansion of ${(1 + x)^{18}}$ are equal, then$ r=$
The coefficient of $x^{4}$ is the expansion of $\left(1+\mathrm{x}+\mathrm{x}^{2}\right)^{10}$ is
Find the middle terms in the expansions of $\left(3-\frac{x^{3}}{6}\right)^{7}$
The sum of the coefficient of $x^{2 / 3}$ and $x^{-2 / 5}$ in the binomial expansion of $\left(x^{2 / 3}+\frac{1}{2} x^{-2 / 5}\right)^9$ is :
If the sum of the coefficients in the expansion of ${(x + y)^n}$ is $1024$, then the value of the greatest coefficient in the expansion is