In the expansion of ${\left( {3x - \frac{1}{{{x^2}}}} \right)^{10}}$ then $5^{th}$ term from the end is :-
$\frac{{17010}}{{{x^6}}}$
$\frac{{17010}}{{{x^9}}}$
$\frac{{17010}}{{{x^8}}}$
$\frac{{17010}}{{{x^{-1}}}}$
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 coefficient of $\frac{1}{x}$ in the expansion of ${\left( {1 + x} \right)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ is :-
If the fourth term in the expansion of $\left(x+x^{\log _{2} x}\right)^{7}$ is $4480,$ then the value of $x$ where $x \in N$ is equal to
The expression $[x + (x^3-1)^{1/2}]^5 + [x - (x^3-1)^{1/2}]^5$ is a polynomial of degree :
The middle term in the expansion of ${\left( {x + \frac{1}{{2x}}} \right)^{2n}}$, is