Actually option 2 is given as answer.So,other options are incorrect.I got an counter example for other options that they are not true.But I am unable to find a counter example to show option 4 is incorrect.
That is ,I need a continuous and one-one function $f:\mathbb{R} \to \mathbb{R}$ such that $f$ is not unbounded i.e. bounded.
Take e.g. the inverse tangent function $\arctan$. It is injective and defined on the entire real number line but its range is $[-\pi/2, \pi/2]$.