(c) When $\theta = 180{^\circ}$, the particle will be at diametrically opposite point, where its velocity is opposite to the initial directions of motion. The change in momentum $= mv - ( - mv) = 2mv$ (maximum). When $\theta = 360{^\circ}$, the particle is at the initial position with momentum $m$. Change in momentum $mv - mv = 0$ (minimum)