The motion of a charged particle in a constant $\vec{B}$

1. is time-reversal invariant
2. is not time-reversal invariant

This question is an advanced level question. But it is easy to answer, if one keeps in mind the following definition. Time-reversal invariance: if any possible motion played backwards is also a possible motion, then the system is time-reversal invariant.

The motion of a charged particle in a constant $\vec{B}$

1. conserves the mechanical energy
2. does not conserve the mechanical energy

The work energy “theorem”

The work energy theorem, $\Delta T = W$ where $T$ is the kinetic energy (and $\Delta T = T_2 - T_1$ is its change) and $W$ is the net work done on the particle, is

1. always valid (in classical mechanics).
2. valid only for conservative forces.