${16^{th}}$ term in the expansion of ${(\sqrt x - \sqrt y )^{17}}$ is

If coefficient of ${(2r + 3)^{th}}$ and ${(r - 1)^{th}}$ terms in the expansion of ${(1 + x)^{15}}$ are equal, then value of r is

In the expansion of ${({5^{1/2}} + {7^{1/8}})^{1024}}$, the number of integral terms is

If the constant term in the binomial expansion of $\left(\frac{x^{\frac{5}{2}}}{2}-\frac{4}{x^{\ell}}\right)^9$ is $-84$ and the Coefficient of $x^{-3 \ell}$ is $2^\alpha \beta$, where $\beta < 0$ is an odd number, Then $|\alpha \ell-\beta|$ is equal to

If the coefficients of $x^{-2}$ and $x^{-4}$ in the expansion of ${\left( {{x^{\frac{1}{3}}} + \frac{1}{{2{x^{\frac{1}{3}}}}}} \right)^{18}}\,,\,\left( {x > 0} \right),$ are $m$ and $n$  respectively, then $\frac{m}{n}$ is equal to