JEE MATHEMATICS MCQ: FUNCTIONS

Which of the following statement is true $(\mathrm{T})$ or false $(\mathrm{F})$ for the function $f: \mathrm{R} \rightarrow \mathrm{R}$ ?
(i) If $|f(x)-f(y)| \leq 30|x-y|, \forall x, y \in \mathrm{R}$, then $f$ is a continuous function on $\mathrm{R}$.
(ii) If $|f(x)-f(y)| \leq 30|x-y|, \forall x, y \in \mathrm{R}$, then $f$ is differentiable on $\mathrm{R}$.
(iii) If $|f(x)-f(y)| \leq 21|x-y|^2, \forall x, y \in \mathbb{R}$, then $f$ is differentiable on $\mathrm{R}$.
(iv) If $|f(x)-f(y)| \leq 21|x-y|^2, \forall x, y \in \mathrm{R}$, then $f$ is a constant function.