Let's evaluate each statement about the olfactory pathway:
(A) The sites of olfactory transduction are the olfactory hairs: Olfactory receptor neurons have cilia, known as olfactory hairs, that extend into the mucus layer of the nasal cavity. These hairs contain receptor proteins that bind to odorant molecules, initiating the process of olfactory transduction. Thus, statement (A) is true.
(B) The olfactory bulbs transmit impulses to the temporal lobe of the cerebral cortex: Olfactory information travels from the olfactory bulbs via the olfactory tracts to several brain regions, including the olfactory cortex, which is located in the temporal lobe (specifically the piriform cortex). Thus, statement (B) is true.
(C) The axons of olfactory receptors pass through the olfactory foramina in the cribriform plate of ethmoid bone: The olfactory receptor neurons are located in the olfactory epithelium in the nasal cavity. Their unmyelinated axons bundle together to form the olfactory nerves (cranial nerve I), which pass through small holes (olfactory foramina) in the cribriform plate of the ethmoid bone to reach the olfactory bulbs in the cranial cavity. Thus, statement (C) is true.
(D) The olfactory nerves are bundles of axons that terminate in the olfactory tracts: The olfactory nerves (bundles of axons of first-order neurons) synapse with second-order neurons (mitral and tufted cells) in the olfactory bulbs. The axons of these second-order neurons then form the olfactory tracts, which project to the olfactory cortex and other brain regions. Therefore, the olfactory nerves do not terminate in the olfactory tracts; they synapse in the olfactory bulbs, and the axons of the postsynaptic neurons form the tracts. Thus, statement (D) is false.
(E) Within the olfactory bulbs the first order neurones synapses with the second order neurones: As mentioned above, the olfactory receptor neurons (first-order neurons) synapse with mitral and tufted cells (second-order neurons) within the glomeruli of the olfactory bulbs. Thus, statement (E) is true.
Based on the analysis, statements (A), (C), and (E) are true.