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
$11$
$10$
$12$
$8$
$x^r$ occurs in the expansion of ${\left( {{x^3} + \frac{1}{{{x^4}}}} \right)^n}$ provided -
The term independent of $x$ in the expansion of $\left( {\frac{1}{{60}} - \frac{{{x^8}}}{{81}}} \right).{\left( {2{x^2} - \frac{3}{{{x^2}}}} \right)^6}$ is equal to
The coefficient of $x^{13}$ in the expansion of $(1 -x)^5(1 + x + x^2 + x^3)^4$ is :-
Show that the middle term in the expansion of $(1+x)^{2 n}$ is
$\frac{1.3 .5 \ldots(2 n-1)}{n !} 2 n\, x^{n},$ where $n$ is a positive integer.
If in the expansion of ${(1 + x)^m}{(1 - x)^n}$, the coefficient of $x$ and ${x^2}$ are $3$ and $-6$ respectively, then m is