An object moving on a horizontal, frictionless surface makes a glancing collision with another object initially at rest on the surface. In this case, which of the following is true about momentum and kinetic energy?
a. Momentum is always conserved, and kinetic energy may be conserved.
b. Kinetic energy is always conserved, and momentum may be conserved.
c. Momentum is always conserved, and kinetic energy is never conserved.
d. Both momentum and kinetic energy are always conserved.
e. Neither momentum nor kinetic energy is conserved.

Momentum is always conserved, and kinetic energy may be conserved.

Explanation:

For an object moving on a horizontal, frictionless surface which makes a glancing collision with another object initially at rest on the surface, the type of collision experienced by this objects can either be elastic or an inelastic collision depending on whether the object sticks together after collision or separates and move with a common velocity after collision.

If the body separates and move with a common velocity after collision, the collision is elastic but if they sticks together after collision, the collision is inelastic.

Either ways the momentum of the bodies are always conserved since they will always move with a common velocity after collision but their kinetic energy may or may not be conserved after collision, it all depends whether they separates or stick together after collision and since we are not told in question whether or not they separate, we can conclude that their kinetic energy "may" be conserved.