Which of the following are correct?

Options

A. For a small deformation of a material, the ratio (stress/ strain) remains same.
B. For a large deformation of a material, the ratio (stress/ strain) decreases.
C. Two wires made of different materials, having the same diameter and length are connected end to end. A force is applied. This stretches their combined length by `2 mm`. Now, the strain is same in both the wire but stress is different.
D. None of these is correct.

Explanation

To solve the question regarding the correctness of the given statements, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Analyze Option A**:
- **Statement**: For small deformation of material, the ratio of stress by strain remains the same.
- **Explanation**: In the elastic region of a material, when the deformation is small and within the elastic limits, the relationship between stress and strain is linear. This means that the ratio of stress to strain (stress/strain) is constant and equal to Young's modulus.
- **Conclusion**: **Option A is correct.**

2. **Analyze Option B**:
- **Statement**: For large deformation of the material, the ratio of stress by strain decreases.
- **Explanation**: When a material undergoes large deformation that exceeds its elastic limit, it may enter the plastic region where the relationship between stress and strain is no longer linear. As the material deforms more, the ability to resist further deformation decreases, leading to a decrease in the ratio of stress to strain.
- **Conclusion**: **Option B is correct.**

3. **Analyze Option C**:
- **Statement**: Two wires made of different materials having the same diameter and length are connected end-to-end. The strain in both wires is the same, but the stress is different.
- **Explanation**: When two wires are connected end-to-end, they experience the same force and therefore the same stress. However, since they are made of different materials, their Young's moduli will differ, leading to different strains. Thus, the strain cannot be the same if the materials are different.
- **Conclusion**: **Option C is incorrect.**

4. **Analyze Option D**:
- **Statement**: None of these.
- **Explanation**: Since we have already established that Options A and B are correct, this statement is false.
- **Conclusion**: **Option D is incorrect.**

### Final Answer:
The correct options are **A and B**.