In the binomial expansion of ${(a - b)^n},\,n \ge 5,$ the sum of the $5^{th}$ and $6^{th}$ terms is zero. Then $\frac{a}{b}$ is equal to
$\frac{1}{6}(n - 5)$
$\frac{1}{5}(n - 4)$
$\frac{5}{{(n - 4)}}$
$\frac{6}{{(n - 5)}}$
The coefficients of three consecutive terms of $(1+x)^{n+5}$ are in the ratio $5: 10: 14$. Then $n=$
The coefficient of $x^5$ in the expansion of $\left(2 x^3-\frac{1}{3 x^2}\right)^5$ is
If the expansion of ${\left( {{y^2} + \frac{c}{y}} \right)^5}$, the coefficient of $y$ will be
In the expansion of ${\left( {{x^2} - 2x} \right)^{10}}$, the coefficient of ${x^{16}}$ is
The coefficients of three successive terms in the expansion of ${(1 + x)^n}$ are $165, 330$ and $462$ respectively, then the value of n will be