Consider the following statements: 1. f(x)=[x] , where [.] is the...

From statement-1 From the definition of greatest integer function $f(x)=[x]$ is discontinuous at $x=n$ for any value of $n \in \mathbb{Z}\therefore \quad$ Statement 1 is correct From statement-2 $\mathrm{f}(\mathrm{x})=\cot \mathrm{x}$ for $x=\pi=\cot \pi=-\infty$ for $\mathrm{x}=2 \pi\mathrm{f}(2 \pi)=\cot 2 \pi=-\infty$ Hence the function $f(x)=\cot x$ is discontinuous at $\mathrm{x}=\mathrm{n} \pi$ where $\mathrm{n} \in \mathrm{Z}$. $\therefore \quad$ Option (C) is correct.