During inelastic collision between two bodies, which of the following quantities always remain conserved? (a) Total kinetic energy (b) Total mechanical energy (c) Total linear momentum (d) Speed of each body

Ans: (c) If in collision kinetic energy after collision ≠ kinetic energy before collision, then the collision is said to be inelastic collision. 

Coefficient of restitution 0 < e < 1

When we are considering the two bodies as system then, the total external force on the system will be zero. 

Hence,the total linear momentum of the system remain conserved.

Here kinetic energy appear in the other forms, i.e. energy may be lost in the form of heat, sound etc. In some cases (K•E) < (K•E) such as when initial K•E is converted into conserved energy of the product (as heat, elastic or excitation) while in other cases (K•E) > (K•E) such as when internal energy stored in the colliding particles is released. 

Ex: (1) Collision b/w two billiard balls.

(2) Collision b/w two automobiles on the road.

In fact all majority of the collisions belong to this category.