In the expansion of ${\left( x - \frac{1}{x} \right)^6}$,the constant term is

If $A$ and $B$ are coefficients of $x^{n}$ in the expansions of $(1+x)^{2n}$ and $(1+x)^{2n-1}$ respectively, then $A / B$ is equal to

The number of rational terms in the binomial expansion of ${\left( 7^{\frac{1}{7}} + 11^{\frac{1}{11}} \right)^{711}}$ is:

Let $\alpha > 0, \beta > 0$ be such that $\alpha^{3} + \beta^{2} = 4$. If the maximum value of the term independent of $x$ in the binomial expansion of $(\alpha x^{\frac{1}{9}} + \beta x^{-\frac{1}{6}})^{10}$ is $10k$,then $k$ is equal to

The second,third and fourth terms in the binomial expansion $(x+a)^n$ are $240, 720$ and $1080$ respectively. Find $x, a$ and $n$.

If the coefficients of $3$ consecutive terms in the expansion of $(1+x)^{23}$ are in arithmetic progression,then those terms are