Statement-I: Two particles moving in the same direction do not lose...

Let masses $m_1, m_2$ have initial velocities $u_1, u_2$ in the same direction and they stick after collision (perfectly, inelastic). Common velocity (v=$\frac{m_1 u_1+m_2 u_2}{m_1+m_2}$) Initial KE: (K_i=$\frac{1}{2}$m_1 u_1^2+$\frac{1}{2}$m_2 u_2^2,) Final KE: (K_f=\frac{1}{2}\left(m_1+m_2\right) v²) Loss of kinetic energy ($\Delta$K=K_i-K_f=\frac{1}{2} \frac{m_1 m_2}{m_1+m_2}\left(u_1-u_2\right)^2 \geq 0) This loss is not the whole initial energy except when $u_1=u_2$ (then ($\Delta$K=0)). So Statement-1 is true: they do not lose all their energy in general. Statement-II is also true: momentum is conserved in all collisions provided the system is isolated (no externa impulse). That includes elastic, inelastic, perfectly inelastic collisions and explosions (internal forces only). So both are true $→$ option (1).