Which of the following is true for carbon suboxide $C_3O_2$?

The value of $\lim_{n \rightarrow \infty} \frac{1}{n^3} \sum_{k=1}^n (k^2 x)$ is

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=|x|$ and $g(x)=[x-3]$ for $x \in R$,then $\{g(f(x)):-\frac{8}{5} < x < \frac{8}{5}\}$ is equal to

$MgCl_2 \cdot 6H_2O$ when heated gives

The $IUPAC$ name of the following compound is

An organic compound $X$ on treatment with pyridinium chlorochromate in dichloromethane gives compound $Y$. Compound $Y$ reacts with $I_2$ and alkali to form triiodomethane. The compound $X$ is