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.

The coefficient of $x^{2012}$ in the expansion of $(1-x)^{2008}\left(1+x+x^2\right)^{2007}$ is equal to

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

In the expansion of ${\left( {\frac{{3{x^2}}}{2} - \frac{1}{{3x}}} \right)^9}$,the term independent of $x$ is

If the ratio of the coefficient of third and fourth term in the expansion of ${\left( {x - \frac{1}{{2x}}} \right)^n}$ is $1 : 2$, then the value of $ n$ will be

In the expansion of ${(1 + 3x + 2{x^2})^6}$ the coefficient of ${x^{11}}$ is