In the expansion of ${\left( {3x - \frac{1}{{{x^2}}}} \right)^{10}}$ then $5^{th}$ term from the end is :-
$\frac{{17010}}{{{x^6}}}$
$\frac{{17010}}{{{x^9}}}$
$\frac{{17010}}{{{x^8}}}$
$\frac{{17010}}{{{x^{-1}}}}$
If the coefficient of ${x^7}$ in ${\left( {a{x^2} + \frac{1}{{bx}}} \right)^{11}}$ is equal to the coefficient of ${x^{ - 7}}$ in ${\left( {ax - \frac{1}{{b{x^2}}}} \right)^{11}}$, then $ab =$
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 middle term in the expansion of ${\left( {x + \frac{1}{{2x}}} \right)^{2n}}$, is
Find the cocfficient of $x^{5}$ in $(x+3)^{8}$
If the coefficients of $x^4, x^5$ and $x^6$ in the expansion of $(1+x)^n$ are in the arithmetic progression, then the maximum value of $n$ is :