For inelastic collision between two spherical rigid bodies

the total kinetic energy is conserved

the total mechanical energy is not conserved

the linear momentum is not conserved

the linear momentum is conserved

Answer

the linear momentum is conserved

In an inelastic collision, the particles do not regain their shape and size completely after collision. Some fraction of mechanical energy is retained by the colliding particles in the form of deformation potential energy. Thus, the kinetic energy of particles no longer remains conserved. However in the absence of external forces, law of conservation of linear momentum still holds good.