The coefficient of $x^{37}$ in the expansion of $(1-x)^{30} \, (1 + x + x^2)^{29}$ is :

If the coefficients of $x^{7}$ in $\left(x^{2}+\frac{1}{b x}\right)^{11}$ and $x^{-7}$ in $\left(x-\frac{1}{b x^{2}}\right)^{11}, b \neq 0$, are equal, then the value of $b$ is equal to:

Expand using Binomial Theorem $\left(1+\frac{ x }{2}-\frac{2}{ x }\right)^{4}, x \neq 0$

${r^{th}}$ term in the expansion of ${(a + 2x)^n}$ is

The coefficient of ${x^n}$in expansion of $(1 + x)\,{(1 - x)^n}$ is

If coefficients of $2^{nd}$, $3^{rd}$ and $4^{th}$ terms in the binomial expansion of ${(1 + x)^n}$ are in $A.P.$, then ${n^2} - 9n$ is equal to