Explanation:

In the field of engineering, failure theories are used to predict the failure of materials or structures under different stress conditions. These theories provide guidelines for determining the safety and design limits of a material or structure.

The given question states that all the theories of failure will give nearly the same result under certain conditions. Let's analyze each option to understand why option 'A' is the correct answer.

a) When one of the principal stresses at a point is large in comparison to the other:
In this case, the stress state is considered to be uniaxial or dominated by one principal stress. When one principal stress is significantly larger than the others, the failure of the material or structure is primarily governed by this dominant stress. Under such conditions, all failure theories, regardless of their specific assumptions and equations, will provide similar results because they are essentially addressing the same fundamental failure mechanism.

b) When shear stresses act:
Shear stresses play a significant role in failure, especially in materials or structures that are subjected to complex loading conditions. However, different failure theories may consider shear stresses differently in their equations and assumptions. Therefore, the results obtained from different failure theories may vary when shear stresses act.

c) When both the principal stresses are numerically equal:
When both principal stresses are numerically equal, the stress state is called biaxial. In this case, different failure theories may provide different results because they may have different assumptions and equations for biaxial stress conditions.

d) For all situations of stress:
This option is too broad and general. Different failure theories are developed to address specific stress conditions and failure mechanisms. Therefore, it is not accurate to say that all failure theories will provide nearly the same result for all situations of stress.

Conclusion:
From the given options, it is evident that option 'A' is the correct answer. When one of the principal stresses at a point is large in comparison to the other, the failure of the material or structure is primarily governed by this dominant stress. Consequently, all failure theories, regardless of their specific assumptions and equations, will provide similar results as they are addressing the same fundamental failure mechanism.