A ball is thrown vertically upwards (relative to the train) in a compartment of a moving train. The face of the person sitting inside the compartment is towards engine of the train.

The correct options are
A The ball will maintain the same horizontal velocity as that of the person (or the compartment) at the time of throwing.
B If the ball appears to be moving backward to the person sitting in the compartment it means that speed of the train is increasing.
D If the ball appears to be moving ahead of the person sitting in the compartment it means the train's motion is retarding.
At the time of throwing the ball, it inherits velocity of platform at that moment . And, the horizontal velocity of the ball is constant in the air, because no acceleration in horizontal direction for ball. If train is accelerating in forward direction then from frame of train, the ball has horizontal component of acceleration in backward direction and vice versa.