The oxidation states of group 14 elements, also known as the carbon group, depend on the number of valence electrons they have. The group 14 elements include carbon (C), silicon (Si), germanium (Ge), tin (Sn), and lead (Pb). Let's analyze each option to determine which oxidation states are exhibited by these elements.

a) Option 'a' suggests that group 14 elements exhibit oxidation states of 1 and 5. However, this is incorrect because none of the elements in this group commonly exhibit an oxidation state of 1 or 5.

b) Option 'b' suggests that group 14 elements exhibit oxidation states of 5 and 2. While some group 14 elements can exhibit an oxidation state of 2, such as tin in Sn(II) compounds, the oxidation state of 5 is not commonly observed for these elements.

c) Option 'c' suggests that group 14 elements exhibit oxidation states of 2 and 4. This is the correct answer. Group 14 elements generally exhibit an oxidation state of 4, where they share or gain four electrons to achieve a stable octet configuration. Silicon, for example, commonly exhibits an oxidation state of +4 in compounds such as SiO2 (silicon dioxide). Group 14 elements can also exhibit an oxidation state of 2, where they lose two electrons to achieve a stable configuration. Tin, for instance, can exhibit an oxidation state of +2 in compounds such as SnCl2 (tin(II) chloride).

d) Option 'd' suggests that group 14 elements exhibit oxidation states of 3 and 5. However, neither oxidation state of 3 nor 5 is commonly observed for these elements.

In summary, the correct answer is option 'c' as group 14 elements primarily exhibit oxidation states of 2 and 4.