For a collision between two particles,which of the following quantities is generally conserved?

Three blocks $A, B$ and $C$ are lying on a smooth horizontal surface,as shown in the figure. $A$ and $B$ have equal masses $m$,while $C$ has mass $M$. Block $A$ is given an initial speed $v$ towards $B$,due to which it collides with $B$ perfectly inelastically. The combined mass then collides with $C$,also perfectly inelastically. If $5/6^{th}$ of the initial kinetic energy is lost in the whole process,what is the value of $M/m$?

$A$ block $C$ of mass $m$ is moving with velocity $v_0$ and collides elastically with block $A$ of mass $m$ which is connected to another block $B$ of mass $2m$ through a spring of spring constant $k$. What is $k$ if $x_0$ is the compression of the spring when the velocity of $A$ and $B$ is the same?

Two identical blocks $A$ and $B$,each of mass $m$,resting on a smooth floor,are connected by a light spring of natural length $L$ and spring constant $k$. The spring is at its natural length. $A$ third identical block $C$ (mass $m$) moving with a speed $v$ along the line joining $A$ and $B$ collides with $A$. The maximum compression in the spring is proportional to

$A$ machine with efficiency $2/3$ uses $12 \text{ J}$ of energy to lift a $2 \text{ kg}$ block to a certain height. If the block is allowed to fall freely from that height,what is its velocity when it reaches the ground?

$A$ constant force of $5 N$ accelerates a stationary particle of mass $500 g$ through a displacement of $5 m$. The average power delivered is: (in $W$)