If the coefficients of the middle terms in the binomial expansions of $(1+\alpha x)^{26}$ and $(1-\alpha x)^{28}, \alpha \neq 0$, are equal, then the value of $\alpha$ is:

The coefficient of $x^2$ in the expansion of $\left(2 x^2+\frac{1}{x}\right)^{10}, x \neq 0$, is :

In the expansion of $\left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}, x>0$, if the term independent of $x$ is (221)k, then k is equal to:

Let the smallest value of $k \in \mathbb{N}$, for which the coefficient of $x^3$ in $(1+x)^3+(1+x)^4+(1+x)^5+\ldots+(1+x)^{99}+(1+k x)^{100}, x \neq 0$, is $\left(43 n+\frac{101}{4}\right)\left({ }^{100} \mathrm{C}_3\right)$ for some $n \in \mathrm{~N}$, be $p$. Then the value of $p+n$ is :