The term independent of $x$ in ${\left( {2x - \frac{1}{{2{x^2}}}} \right)^{12}}$is
$-7930$
$-495$
$495$
$7920$
The ratio of the coefficient of $x^{15}$ to the term independent of $x$ in the expansion of ${\left( {{x^2} + \frac{2}{x}} \right)^{15}}$ is
The ratio of the coefficient of terms ${x^{n - r}}{a^r}$and ${x^r}{a^{n - r}}$ in the binomial expansion of ${(x + a)^n}$ will be
The greatest term in the expansion of $\sqrt 3 {\left( {1 + \frac{1}{{\sqrt 3 }}} \right)^{20}}$ is
If the second term of the expansion ${\left[ {{a^{\frac{1}{{13}}}}\,\, + \,\,\frac{a}{{\sqrt {{a^{ - 1}}} }}} \right]^n}$ is $14a^{5/2}$ then the value of $\frac{{^n{C_3}}}{{^n{C_2}}}$ is :
The coefficient of ${x^{32}}$ in the expansion of ${\left( {{x^4} - \frac{1}{{{x^3}}}} \right)^{15}}$ is