Which of these is true of an inelastic collision between two objects in a closed system but not of an elastic collision? total momentum is conserved. total kinetic energy is conserved. kinetic energy is less after the collision. total momentum is not conserved.

The correct answer is "Kinetic energy is less after the collision. "
In fact, in an elastic collision, both momentum and kinetic energy are conserved. Instead, for an inelastic collision, the momentum is still conserved, while the kinetic energy is not: part of it is lost during the collision (mainly because of internal frictions), and therefore the value of the total kinetic energy of the system after the collision is less than its value before the collision.