To maintain a speed of $80\,km/h$ by a bus of mass $500\,kg$ on a plane rough road for $4\,km$ distance,the work done by the engine of the bus will be $........\,kJ$. [The coefficient of friction between the tyre of the bus and the road is $0.04$].

$A$ bullet of mass $4\,g$ is fired horizontally with a speed of $300\,m/s$ into a $0.8\,kg$ block of wood at rest on a table. If the coefficient of friction between the block and the table is $0.3$,how far will the block slide approximately (in $,m$)?

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-$1$: $A$ point particle of mass $m$ moving with speed $u$ collides with a stationary point particle of mass $M$. If the maximum energy loss possible is given as $f \left( \frac{1}{2} m u^2 \right)$, then $f = \left( \frac{m}{M + m} \right)$.
Statement-$2$: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

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 $M/m$?

$A$ man throws a ball to a height of $12 \ m$,where it reaches with a speed of $12 \ m/s$. If the man throws the ball such that it just reaches this height,what percentage of energy would he have saved?

$A$ ball of mass $0.2 \ kg$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2 \ m$ while applying the force and the ball goes up to $2 \ m$ height further,find the magnitude of the force $F$ in $N$. (Consider $g = 10 \ m/s^2$)