If $A$ and $B$ are the coefficients of $x^n$ in the expansions of $(1 + x)^{2n}$ and $(1 + x)^{2n - 1}$ respectively,then

The greatest term in the expansion of $(1+x)^{15}$,when $x=\frac{1}{2}$ is

Find $a$ if the $17^{\text{th}}$ and $18^{\text{th}}$ terms of the expansion $(2 + a)^{50}$ are equal.

If $C_j$ stands for ${}^nC_j$,then $\frac{C_1}{C_0} + \frac{2 \times C_2}{C_1} + \frac{3 \times C_3}{C_2} + \ldots + \frac{n \times C_n}{C_{n-1}} = $

If the coefficients of the $(2r + 4)^{th}$ and $(r - 2)^{th}$ terms in the expansion of $(1 + x)^{18}$ are equal,then $r =$

If $n$ is the degree of the polynomial,$\left[ {\frac{1}{{\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8 + \left[ {\frac{1}{{\sqrt {5{x^3} + 1} + \sqrt {5{x^3} - 1} }}} \right]^8$ and $m$ is the coefficient of $x^{12}$ in it,then the ordered pair $(n, m)$ is equal to