Coefficient of $x^{11}$ in the expansion of $\left(1+x^2\right)^4\left(1+x^3\right)^7\left(1+x^4\right)^{12}$ 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

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

Let the coefficients of three consecutive terms in the binomial expansion of $(1+2 x)^{ n }$ be in the ratio $2: 5: 8$. Then the coefficient of the term, which is in the middle of these three terms, is $………..$.

The coefficient of ${x^3}$ in the expansion of ${\left( {x – \frac{1}{x}} \right)^7}$ is