Binomial Theore...

The seventh term in the expansion of
$$ \left(4x-\dfrac{1}{2\sqrt{x}}\right)^{13} $$ is

The coefficients of $$ x^p $$ and $$ x^q $$ ($$p$$ and $$q$$ are positive integers) in the expansion of $$ (1 + x)^{p+q} $$ are

In the expansion of $$ (3+ax)^9 $$ coefficients of $$ x^2 $$ and $$ x^3 $$ are equal then $$a =$$

If the coefficient of $$ x^7 $$ in $$(ax^2 + \dfrac{1}{bx})^{11} $$ is equal to the coefficient of $$ x^{-7} $$ in $$ (ax - \dfrac{1}{bx^2})^{11} $$ then

If the fourth term in the expansion of $$\left  (px+\dfrac{1}{x}\right)^n $$ is $$\dfrac52$$, then $$(n, p) = $$

In the binomial expansion of $$ \left (  \sqrt{y} + \dfrac{1}{2\sqrt[4]{y}} \right )^8 $$, the terms in the expansion in which the power of $$y$$ is a natural number are:

In the expansion of $$ (2+\dfrac{x}{3})^n $$, coefficients of $$ x^7 $$ and $$ x^8 $$ are equal. Then $$ n = $$

The middle term in the expansion of $$ \left (\displaystyle \frac{x^{\frac{3}{2}}}{\sqrt{a}} - \frac{y^{\frac{5}{2}}}{b^{\frac{3}{2}}} \right )^8 $$ is 

The middle term in the expansion of $$ \left ( x + \dfrac{1}{x} \right )^{10} $$ is

The middle term in the expansion of $$ (1+x)^{2n} $$ is