TargetIIT

as rod is hinged,

using cons. of ang. momentum,

mul = mvl + Ml[p]2[/p]ω/3 ... (i)  (v = vel. of particle after collision, ω=ang vel. of rod)

using COR eqn:

ωl-v = u .... (ii)

So u can solve for ω and v..
which solves first two parts.

To find impulsive reaction at A,
draw the FBD of the rod and of the particle during the collision (remember hinge will give both hori and vertical reaction)