(c) the frame may be inertial but the resultant force on the particle is zero
(d) the frame may be non-inertial but there is a non-zero resultant force
According to Newton's second law which says that net force acting on the particle is equal to rate of change of momentum ( or mathematically F = ma), so if a particle is at rest then Fnet = ma = m.
Now, if the frame is inertial, then the resultant force on the particle is zero.
If the frame is non-inertial,
vector sum of all the forces plus a pseudo force is zero.
i.e. Fnet ≠ 0.