${r^{th}}$ term in the expansion of ${(a + 2x)^n}$ is
$\frac{{n(n + 1)....(n - r + 1)}}{{r!}}{a^{n - r + 1}}{(2x)^r}$
$\frac{{n(n - 1)....(n - r + 2)}}{{(r - 1)\,!}}{a^{n - r + 1}}{(2x)^{r - 1}}$
$\frac{{n(n + 1)....(n - r)}}{{(r + 1)!}}{a^{n - r}}{(x)^r}$
None of these
If $p$ and $q$ be positive, then the coefficients of ${x^p}$ and ${x^q}$ in the expansion of ${(1 + x)^{p + q}}$will be
The coefficient of $x^{2012}$ in the expansion of $(1-x)^{2008}\left(1+x+x^2\right)^{2007}$ is equal to
If $n$ is the degree of the polynomial,
${\left[ {\frac{1}{{\sqrt {5{x^3} + 1} - \sqrt {5{x^3} - 1} }}} \right]^8} $$+ {\left[ {\frac{1}{{\sqrt {5{x^3} + 1} + \sqrt {5{x^3} - 1} }}} \right]^8}$ and $m$ is the coefficient of $x^{12}$ in it, then the ordered pair $(n, m)$ is equal to
Coefficient of $x^3$ in the expansion of $(x^2 - x + 1)^{10} (x^2 + 1 )^{15}$ is equal to
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.