The brightness on Earth of such celestial bodies like stars invariably depends both on the radius of the luminescent object and its temperature.
This question requires understanding of multiple concepts such as:
1. Use of like Vs as( like can't be used to show examples whereas 'as'/such as is used for giving examples.
2. Parallelism. (Use of word pair i.e not only- but also with parallel structure)
A. like stars invariably depends both on the radius of the luminescent object and its temperature// can't use like for giving examples//
B. like stars invariably depends both on the radius of the luminescent object and on its temperature//same as A//
C. as stars invariably depends on both the radius of the luminescent object and on its temperature// Follow rule 1 but violates rule 2 because it is not parallel. It would be correct if 'on both X and Y' and not 'on both X and on Y'
D. as stars invariably depends both on the radius of the luminescent object and its temperature//same as C//
E. as stars invariably depends both on the radius of the luminescent object and on its temperature//correct because parallel and use of such as for giving examples//