The correct answer is option 'A' (i), (ii), and (iii). Let's discuss each statement in detail:

(i) Cell-mediated immunity is responsible for acquired immunity:
Cell-mediated immunity is one of the two arms of acquired immunity, the other being humoral immunity. Acquired immunity is the immunity that develops after exposure to an antigen. Cell-mediated immunity involves the activation of T lymphocytes, which directly attack infected cells or cancer cells. These T cells recognize antigens presented by antigen-presenting cells (APCs) and initiate an immune response.

(ii) It produces a primary response of low intensity:
The primary immune response is the initial response of the immune system to an antigen. It occurs when the immune system encounters a specific antigen for the first time. During the primary response, there is a lag period before antibodies are produced, and the intensity of the response is relatively low. It takes time for B cells to differentiate into plasma cells and secrete antibodies. However, the primary response leads to the development of memory cells, which are responsible for faster and stronger secondary immune responses upon subsequent exposure to the same antigen.

(iii) Active and passive immunity are types of acquired immunity:
Active immunity is the immunity that develops in response to an antigen exposure. It can occur naturally through infection or artificially through vaccination. When a person is exposed to an antigen, their immune system produces antibodies and memory cells, providing long-term protection against that specific antigen.

Passive immunity, on the other hand, is the temporary immunity that is acquired from another source. It can be acquired naturally, such as the transfer of antibodies from a mother to her fetus through the placenta or breast milk, or artificially, through the administration of preformed antibodies (e.g., immune globulins). Passive immunity provides immediate but short-lived protection, as the transferred antibodies are eventually cleared from the body.

(iv) Polymorphonuclear leucocytes and natural killer cells are involved in acquired immunity:
This statement is incorrect. Polymorphonuclear leukocytes, such as neutrophils, basophils, and eosinophils, are mainly involved in innate immunity, the non-specific defense mechanism that provides immediate, but short-lived protection against a wide range of pathogens. Natural killer (NK) cells are also part of the innate immune system and play a role in the early defense against viral infections and some types of cancer cells. However, acquired immunity primarily involves the activation of lymphocytes, including B cells and T cells.

In conclusion, the correct statements regarding the characteristics of acquired immunity are (i) Cell-mediated immunity is responsible for acquired immunity, (ii) It produces a primary response of low intensity, and (iii) Active and passive immunity are types of acquired immunity.