If $p$ is an integral multiple of $4$ lying between the coefficients of $x^4$ and $x$ in the expansion of $\left(x^2+\frac{1}{x}\right)^8$,then the number of such values of $p$ is

If the coefficient of the $3^{\text{rd}}$ term from the beginning in the expansion of $\left(ax^2 - \frac{8}{bx}\right)^9$ is equal to the coefficient of the $3^{\text{rd}}$ term from the end in the expansion of $\left(ax - \frac{2}{bx^2}\right)^9$,then the relation between $a$ and $b$ is:

The term independent of $y$ in the expansion of $(y^{-1/6} - y^{1/3})^9$ is

In the expansion of $(1+x)^n$,the coefficients of the $p^{th}$ and $(p+1)^{th}$ terms are respectively $p$ and $q$. Then $p+q$ is equal to:

The two middle terms in the expansion of ${\left( {x - \frac{1}{x}} \right)^{11}}$ are:

If $n \geq 100$ and the coefficient of $x^{100}$ in $1+(1+x)+(1+x)^2+\cdots+(1+x)^n$ is ${ }^{201} C_{101}$,then $n=$