If the coefficient of $x ^{10}$ in the binomial expansion of $\left(\frac{\sqrt{x}}{5^{\frac{1}{4}}}+\frac{\sqrt{5}}{x^{\frac{1}{3}}}\right)^{60}$ is $5^{ k } l$, where $l, k \in N$ and $l$ is coprime to $5$ , then $k$ is equal to
$5$
$6$
$7$
$8$
In the binomial expansion of ${(a - b)^n},\,n \ge 5,$ the sum of the $5^{th}$ and $6^{th}$ terms is zero. Then $\frac{a}{b}$ is equal to
Prove that the coefficient of $x^{n}$ in the expansion of $(1+x)^{2n}$ is twice the coefficient of $x^{n}$ in the expansion of $(1+x)^{2 n-1}$
The middle term in the expression of ${\left( {x - \frac{1}{x}} \right)^{18}}$ is
Find the $r^{\text {th }}$ term from the end in the expansion of $(x+a)^{n}$
Find an approximation of $(0.99)^{5}$ using the first three terms of its expansion.