ANS:D - All the above.

1. Material fails essentially by shear: This statement reflects one of the key principles underlying Mohr's theory of failure. It suggests that the failure of materials, particularly in the context of soil mechanics and geotechnical engineering, primarily occurs due to shear stresses exceeding a critical threshold. Mohr's theory helps engineers understand how materials respond to external loads and predict their failure modes, especially in situations where shear stresses play a significant role.
2. Ultimate strength of the material is determined by the stress in the plane of slip: While this statement is generally true, it's not unique to Mohr's theory. The ultimate strength of a material, particularly in shear, is indeed determined by the stress present in the plane of slip. However, this concept is fundamental in many theories of material failure, not just Mohr's theory.
3. Failure criterion is independent of the intermediate principal stress: This statement is not specific to Mohr's theory and is more aligned with some other failure criteria. While some failure criteria may ignore the influence of the intermediate principal stress, it's not a defining characteristic of Mohr's theory. Mohr's theory considers the influence of all principal stresses on material failure.