Lymphocytes are white blood cells that originate, mature and proliferate in specialised organs known as lymphoid organs.
Bone marrow is considered as a primary lymphoid organ as it is the site for production of all lymphocytes.
Hence, T- lymphocytes originate in the bone marrow. These are immature cells.
The T-lymphocytes migrate to thymus from the bone marrow and undergo maturation in the thymus gland. (a lobed primary lymphoid organ located near the heart and beneath the breastbone).
The T-lymphocytes after maturation migrate to the secondary lymphoid organs like spleen, tonsils, lymph nodes, etc., for proliferation. There they come in contact with trapped antigens, bind with them via specific surface receptors and proliferate by dividing and differentiating into different types of cells like effector cells and memory cells.
Effector T-cells are a group of cells that actively respond to an antigenic stimulus.
Memory T cells are specific to the foreign antigen recognized during the initial immune response. These cells have a memory for that particular antigen and they survive for a long time. They respond quickly during the subsequent exposure to the same antigen.
Thus, only statement I is true while the statements II, III and IV are false.
Figure: Proliferation of T cells