Question

A particle stays at rest as seen in a frame. We can conclude that
(a) the frame is inertial
(b) resultant force on the particle is zero
(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

Answer 1

(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 F_net = ma = m\[\frac{d v}{d t} = m\frac{d (0)}{d t} = m \times 0 = 0\]
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. F_net ≠ 0.