Which of the following points is the likely position of the centre of mass of the system shown in figure?

A particle of mass $$m$$ is moving in $$y z$$-plane with a uniform velocity $$v$$ with its trajectory running parallel to $$+v e y$$-axis and intersecting $$z$$-axis at $$z=a$$ in figure. The change in its angular momentum about the origin as it bounces elastically from a wall at $$y=$$ constant is

When a disc rotates with uniform angular velocity, which of the following is not true?

A uniform square plate has a small piece $Q$ of an irregular shape removed and glued to the centre of the plate leaving a hole behind in figure. The moment of inertia about the $z$-axis is then,

In problem 5, the CM of the plate is now in the following quadrant of x-y plane.