Does perfectly inelastic collision conserve energy if given external energies are negligble?

Question

If in the question given perfectly inelastic collision and assuming heat and sound energy are negligible then Mechanical energy is conserved opposite to the general law?

Answer 1

Does perfectly inelastic collision conserve energy if given external energies are negligble ?

Energy across the whole system and environment is always conserved. If the kinetic energy of the system is the same before and after the collision then the collision is, by definition, elastic and not inelastic.