$A$ molecule in a gas container hits a horizontal wall with speed $200 \; m s^{-1}$ at an angle of $30^{\circ}$ with the normal,and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic?

(A) Yes; the collision is elastic.
$1$. Momentum Conservation: In any collision,the total momentum of the system (molecule + wall) is conserved,provided no external force acts on the system. Since the wall is part of the container and is effectively stationary (or has infinite mass),the momentum of the molecule changes,but the total momentum of the system remains conserved.
$2$. Nature of Collision: The molecule strikes the wall with a speed of $200 \; m s^{-1}$ and rebounds with the same speed of $200 \; m s^{-1}$. Since the kinetic energy of the molecule before the collision is $K_i = \frac{1}{2} m v^2$ and after the collision is $K_f = \frac{1}{2} m v^2$,the kinetic energy remains unchanged $(K_i = K_f)$. Therefore,the collision is elastic.