Supratim, here is my take on this via POE:
(A) A star will compress itself into a white dwarf, a neutron star, or a black hole after it passes through a red giant stage, depending on mass.
- here it is ambigious, is it referring to white dwarf, neuton star or star
(B) After passing through a red giant stage, depending on its mass, a star will compress itself into a white dwarf, a neutron star, or a black hole.
- Sequence of events wrong, Changes meaning, mass has to be determined first before passing through the red giant stage
© After passing through a red giant stage, a star’s mass will determine if it compresses itself into a white dwarf, a neutron star, or a black hole.
-Misplaced modifier issue, 'After passing through a red giant stage' seems to be modifying star's mass , should be the star . Plus carries forward the same problem as in B
(D) Mass determines whether a star, after passing through the red giant stage, will compress itself into a white dwarf, a neutron star, or a black hole.
-Correct choice
(E) The mass of a star, after passing through the red giant stage, will determine whether it compresses itself into a white dwarf, a neutron star, or a black hole.
-Again misplaced modifier issue, 'after passing through the red giant stage' is incorrectly modifying the mass of the star. Plus distorts the meaning to say that the 'mass of the star' is passing through the red giant stage