Is it possible for the kinetic energy of an object not to increase when work is done on it? If so,when?

Two particles,of masses $M$ and $2M$,moving as shown,with speeds of $10\, m/s$ and $5\, m/s$,collide elastically at the origin. After the collision,they move along the indicated directions with speeds $v_1$ and $v_2$ respectively. The values of $v_1$ and $v_2$ are nearly:

Consider the following statements $A$ and $B$. Identify the correct choice in the given answers.
$A$. In an inelastic collision,there is no loss in kinetic energy during collision.
$B$. During a collision,the linear momentum of the entire system of particles is conserved if there is no external force acting on the system.

$A$ ball of mass $m_1$ falls from height $h_1$ from rest to strike a spring of force constant $K$,which forces another ball of mass $m_2$ to jump on a horizontal floor at a height $h_2$ below it. Find the horizontal distance at which the ball of mass $m_2$ strikes the floor from the position of the start. [Assume the spring is fixed and the collision is elastic].

$A$ force of $10 \ N$ acting at an angle on a particle produces a displacement of $(3 \hat{i} - 4 \hat{\jmath}) \ m$. Due to this force,if the kinetic energy of the particle is decreased by $25 \ J$,then the angle between the force and the displacement is:

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 $M/m$?