The field lines of a negative point charge are as shown in the figure. Does the kinetic energy of a small negative charge increase or decrease in going from B to A?      

The electric field present due to the given point charge will be directed towards the centre. A negative charge always experiences a force in the direction opposite to that of the external electric field present; that is away from the centre. This will cause its motion to retard while moving from B to A. Hence, its kinetic energy will decrease in going from B to A.