Starting with option (a), if E = 0, B ≠ 0 then a particle can move with same velocity only if the angle between its velocity and the magnetic field in which it is travelling is having 0o angle between them as force on a moving charged particle is given by F=qv×B where q is charge of the particle, v is velocity of the charged and B is magnitude of the magnetic field.
(b) if E ≠ 0, B ≠ 0. In this case a particle can have same velocity if velocity of the particle, electric field and magnetic field are perpendicular to each other such that the force due to magnetic field and force due to electric field cancel each other. In other words, the Lorentz force equals to zero then only the particle can move with same velocity.
(c) if E ≠ 0, B = 0. In this case the particle can’t move with same velocity as it will experience force due to electric field due to which either it will change its direction or speed or both.
(d) E = 0, B = 0. In this case because the charged particle will not experience any force so it will move with same velocity.
Hence, correct answers are (a), (b) and (d).
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