Let $x_k$ be real numbers such that $x_k\ge k^4+k^2+1$ for $1\le k\le 2018.$ Denote $N=\sum _{k=1}^{2018}k.$ Consider the following inequalities.
I. ${\left(\sum _{k=1}^{2018}k{x}_k\right)}^2\le N\left(\sum _{k=1}^{2018}k{x}_k^2\right)$

II. ${\left(\sum _{k=1}^{2018}k{x}_k\right)}^2\le N\left(\sum _{k=1}^{2018}{k}^2{x}_k^2\right)$
Then,

What is the combined ratio of 3:2, 7:4 and 6:5?

Consider the following statements
I. $\underset{n\to \infty }{\lim }\frac{2^n+(-2{)}^n}{2^n}$ does not exist
II. $\underset{n\to \infty }{\lim }\frac{3^n+(-3{)}^n}{4^n}$ does not exist
Then

In a mixture of $165$ litres, the ratio of liquids $X$ and $Y$ is $6:5$. If $5$ litres of liquid $Y$ is added in the mixture, then what is the ratio of $X$ and $Y$ in the new mixture ?