The correct answer is option 'A', T-lymphocytes.

T-lymphocytes, also known as T cells, are a type of white blood cell that plays a key role in cell-mediated immunity (CMI). CMI is a type of immune response that involves the activation of T cells to target and destroy infected or abnormal cells in the body.

Below is a detailed explanation of how T-lymphocytes mediate CMI:

1. Introduction to T-lymphocytes:
- T-lymphocytes are a type of immune cell that are produced in the bone marrow and mature in the thymus gland.
- They are a critical component of the immune system and play a central role in coordinating immune responses.

2. Cell-Mediated Immunity (CMI):
- Cell-mediated immunity refers to the immune response that involves the activation of immune cells to directly attack and destroy infected or abnormal cells.
- It is primarily mediated by T-lymphocytes.

3. Activation of T-lymphocytes:
- T-lymphocytes are activated when they encounter an antigen, which is a foreign substance or pathogen.
- Antigen-presenting cells, such as macrophages and dendritic cells, present the antigen to T-lymphocytes, triggering their activation.

4. Differentiation of T-lymphocytes:
- Once activated, T-lymphocytes differentiate into different subsets, including cytotoxic T cells (CD8+ T cells) and helper T cells (CD4+ T cells).

5. Cytotoxic T cells:
- Cytotoxic T cells are responsible for directly killing infected or abnormal cells.
- They recognize infected cells by binding to specific antigens presented on the surface of the infected cells.
- Once bound, cytotoxic T cells release cytotoxic molecules, such as perforin and granzymes, to induce cell death in the infected cells.

6. Helper T cells:
- Helper T cells play a crucial role in orchestrating the immune response.
- They release chemical messengers called cytokines that help activate and coordinate other immune cells, such as B-lymphocytes and macrophages.

7. Overall Role of T-lymphocytes in CMI:
- T-lymphocytes, particularly cytotoxic T cells and helper T cells, play a central role in mediating cell-mediated immunity.
- They recognize and destroy infected or abnormal cells directly or assist other immune cells in their immune response.

In conclusion, T-lymphocytes mediate cell-mediated immunity by directly killing infected or abnormal cells (cytotoxic T cells) and coordinating immune responses (helper T cells). Other cell types, such as red blood corpuscles and B-lymphocytes, are not primarily involved in cell-mediated immunity.