If the term independent of $x$ in the exapansion of $\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{9}$ is $k,$ then $18 k$ is equal to

Find the $r^{\text {th }}$ term from the end in the expansion of $(x+a)^{n}$

The coefficient of the middle term in the binomial expansion in powers of $x$ of ${(1 + \alpha x)^4}$ and of ${(1 - \alpha x)^6}$ is the same if $\alpha $ equals

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

In the binomial expansion of ${\left( {a - b} \right)^n},n \ge 5,\;$ the sum of $5^{th}$ and $6^{th}$ terms is zero , then $a/b$ equals.

Let the coefficients of three consecutive terms in the binomial expansion of $(1+2 x)^{ n }$ be in the ratio $2: 5: 8$. Then the coefficient of the term, which is in the middle of these three terms, is $...........$.