(a) The average speed of a particle in a given time is never less than the magnitude of the average velocity.
(b) It is possible to have a situation in which |d(→v)/dt| ≠ 0 but d|→v|/dt = 0.
(c) The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval.
(d) The average velocity of a particle moving on a straight line is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval. (Infinite accelerations are not allowed.)
Pick the correct statements

(a) Average speed of a particle in a given time is never less than the magnitude of the average velocity.

This statement is generally true. Average speed is defined as the total distance traveled divided by the total time taken, and it is always greater than or equal to the magnitude of the average velocity because velocity is a vector that includes both magnitude and direction.
(b) It is possible to have a situation in which |(dv/dt)| ≠ 0 but (d|v|/dt) = 0

This statement is true. It's possible for the magnitude of velocity (|v|) to be constant, meaning its derivative with respect to time (d|v|/dt) is zero, while the direction of the velocity changes, resulting in a non-zero derivative of velocity with respect to time (|(dv/dt)|).
(c) The average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval.

This statement is true. For example, if a particle moves in a closed loop or completes a round trip, its average velocity over the entire journey can be zero, even though its instantaneous velocity is never zero within the interval.
(d) The average velocity of a particle moving on a straight line is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval. (Infinite accelerations are not allowed.)

This statement is not generally true. If a particle's average velocity is zero over a time interval on a straight line, it means the particle traveled the same distance in both directions, and it would imply that the particle reversed direction at some point. In such a case, the instantaneous velocity would be zero at the moment of reversal. However, if the particle maintains a constant velocity in one direction without reversing, the average velocity will not be zero.
So, the correct statements are (a), (b), and (c). Statement (d) is not generally true.