The correct answer is option 1, which states that Hooke`s law is valid only in the proportional region of the stress-strain curve.

Hooke`s law is a fundamental principle in solid mechanics that describes the relationship between the stress applied to a material and the resulting strain. According to Hooke`s law, the stress is directly proportional to the strain for small deformations within the elastic limit of a material. This means that as long as the stress-strain relationship remains linear, Hooke`s law is applicable.

Option 2, which suggests that Hooke`s law is valid for the entire stress-strain curve, is incorrect. Hooke`s law is only valid in the proportional region, where the material behaves elastically and the stress-strain relationship is linear. Beyond this region, the material may exhibit non-linear behavior, such as yielding or plastic deformation.

Option 3, which states that Hooke`s law is valid in the entire elastic region of the stress-strain curve, is also incorrect. The elastic region is a subset of the stress-strain curve, which includes the proportional region where Hooke`s law holds true. However, the elastic region also includes a non-linear region known as the yield point, where the material starts to exhibit plastic deformation.