Anwer carefully, with reasons:
a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact)?
Is the total linear momentum conserved during the short time of an elastic collision of two balls?
c) What are the answers to a) and b) for an inelastic collision?
d) If the potenital energy of two billiard balls depends only on the separation distance between their centers, is the collision elastic or inelastic? (note we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

Explanation

No, as during that short duration the balls are deformed. In fact, during this period, kinetic energy of the balls changes into their potential energy.
Yes, linear momentum is always conserved.
As said earlier, linear momentum is always conserved whether the collision is elastic or inelastic but there occurs a loss in kinetic energy in an inelastic collision.