A boy sitting in a train moving with a uniform velocity drops a coin outside. A man standing outside the train will find the trajectory of the coin to be

Parabola, because when the coin is dropped at a particular point, it has the same velocity as the running train. So by Newton's first law, it continues its motion horizontally with that velocity. But then, it is also pulled down by earth's gravity continuously. In this situation its horizontal motion gives way to the parabolic motion until it reaches the ground.