During inelastic collision between two objects, which of the following quantity always remains
conserved?

Since no external forces are acting on the colliding bodies during collision, thus total linear momentum is always conserved in all type of collisions but kinetic energy in not conserved in all collisions. Kinetic energy is conserved in perfectly elastic collision only but some kinetic energy is lost in inelastic collisions. So, total kinetic energy is not conserved in inelastic collision.