The correct options are
B May move towards the mirror
C May move toward the mirror if the mirror is concave
D Must move toward the mirror if the mirror is convex
If the mirror is concave and a real object is approaching it, the image will move away from the mirror for object distance greater than focal length. If object distance is less than the focal length, virtual image will be formed which moves toward the mirror.
If mirror is convex, as object is approaching the mirror, image will move from focus to pole, i.e., toward the mirror.