The two successive terms in the expansion of $(1+x)^{24}$ whose coefficients are in the ratio $1:4$ are

The coefficient of $x^n$ in the expansion of $(1+x)^{2 n}$ and $(1+x)^{2 n-1}$ are in the ratio

If the coefficients of 2 nd , 3 rd and the 4 th terms in the expansion of $(1+x)^n$ are in AP, then the value of $n$ is

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

If the middle term of $\left(\frac{1}{x}+x \sin x\right)^{10}$ is equal to $7 \frac{7}{8}$, then the value of $x$ is