Which one of the following statements does not hold true when two balls of masses $m_1$ and $m_2$ undergo an elastic collision?

$A$ point mass of $1 \, kg$ collides elastically with a stationary point mass of $5 \, kg$. After their collision, the $1 \, kg$ mass reverses its direction and moves with a speed of $2 \, m/s$. Which of the following statement(s) is (are) correct for the system of these two masses?
$(A)$ Total momentum of the system is $3 \, kg \cdot m/s$
$(B)$ Momentum of $5 \, kg$ mass after collision is $4 \, kg \cdot m/s$
$(C)$ Kinetic energy of the centre of mass is $0.75 \, J$
$(D)$ Total kinetic energy of the system is $4 \, J$

$A$ particle of mass $m$ moving horizontally with velocity $v_0$ strikes a smooth wedge of mass $M$,as shown in the figure. After the collision,the particle starts moving up the inclined face of the wedge and rises to a height $h$. Choose the correct statement$(s)$ related to particle $m$.

$A$ block of mass $m$ slides from rest at a height $H$ on a frictionless inclined plane as shown in the figure. It travels a distance $d$ across a rough horizontal surface with coefficient of kinetic friction $\mu$ and compresses a spring of spring constant $k$ by a distance $x$ before coming to rest momentarily. Then the spring extends and the block travels back attaining a final height of $h$. Then,

$A$ motor engine pumps $1800 \,L$ of water per minute from a well of depth $30 \,m$ and allows it to pass through a pipe of cross-sectional area $30 \,cm^2$. Then the power of the engine is (Acceleration due to gravity,$g=10 \,m/s^2$) (in $\,kW$)

$A$ light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $m_1 = 0.36 \text{ kg}$ and $m_2 = 0.72 \text{ kg}$. Taking $g = 10 \text{ m/s}^2$,find the work done (in joules) by the string on the block of mass $0.36 \text{ kg}$ during the first second after the system is released from rest.