Let for some $\alpha \in \mathbb{R}, f: \mathbb{R} \rightarrow \mathbb{R}$ be a function satisfying $f(x+y)=f(x)+2 y^2+y+\alpha x y$ for all $x, y \in \mathbb{R}$. If $f(0)=-1$ and $f(1)=2$, then the value of $\sum\limits_{n=1}^5(\alpha+f(n))$ is :

Let [•] denote the greatest integer function. If the domain of the function

$f(x)=\cos ^{-1}\left(\frac{4 x+2[x]}{3}\right)$ is $[\alpha, \beta]$, then $12(\alpha+\beta)$ is equal to :

The number of functions $f:\{1,2,3,4\} \rightarrow\{a, b, c\}$, which are not onto, is :

Given below are two statements :

Statement I : The function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = \frac{x}{1 + |x|}$ is one-one.

Statement II : The function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = \frac{x^2 + 4x - 30}{x^2 - 8x + 18}$ is many-one.

In the light of the above statements, choose the correct answer from the options given below :