When no current is passed through a conductor
(This question has multiple correct options)
${\text{A}}{\text{.}}$ the free electrons do not move.
${\text{B}}{\text{.}}$ the average speed of a free electron over a large period of time is zero.
${\text{C}}{\text{.}} $the average velocity of a free electron over a large period of time is zero.
$ {\text{D}}{\text{.}}$ the average velocities of all the free electrons at an instant is zero.

Hint: Even when no current passes through the conductor, the electrons are in a state of random motions, caused by thermal excitement. The random motions, turns their net velocity to be 0.

Complete Step-by-Step solution:
For option (A)-
The free electrons do move even when no current is passing through them because of the thermal energy possessed by the conductor, which excites the electrons.
This option is wrong.

For option (B)-
The average speed of an electron will not be zero, since speed is a scalar quantity and so, even after all the random motions, it does not cancel out.
This is also a wrong option.

For option (C)-
When there is no electric field applied, the electrons move randomly in any direction. The net displacement of an electron is zero. The sum of the velocities which the electron gets in its motion sums to 0. Over a large period, the net or say average velocity of one free electron will become zero.
The option is correct.

For option (D)-
As one free electron has an average velocity equal to zero, the sum of the average velocities of all electrons will add up to zero. So, the average velocity of all electrons will be zero. Another way to look at this is, since there is no current in the conductor it implies that the net displacement of all the electrons has to be 0. This means they will have 0 drift velocity. So, at any instant the average velocities of all the free electrons at any instant will be 0.
This option is correct.

The correct options are (C) and (D).

Note: When an electric field is applied in a conductor, all the electrons drift in the opposite direction of the field and move towards the higher potential. This average velocity of the electrons over a period of time is termed as the drift velocity which is 0 in the static state.