Speed is scalar while Velocity and Acceleration are vectors.

If speed is varying, velocity varies since magnitude of velocity=speed. Therefore, option A is not correct.

If velocity is varying, it is not necessary that speed will also vary since in this case velocity can be varying due to direction only. Therefore, option B is correct.

If velocity is not varying, the acceleration is zero. Therefore, option C is not correct.

If speed is not varying, it is not necessary that velocity will not vary since the direction can vary the velocity and hence acceleration will be non-zero. Therefore, option D is correct.