The centre of mass of a system of two particles divides the distance between them

The figure shows two cylindrical rods whose centers of mass are marked as $A$ and $B$. The line $AB$ divides the region into two parts: one containing point $O$ (region $1$) and the other containing point $O'$ (region $2$). Choose the correct option regarding the center of mass of the combined system.

The velocities of three particles of masses $20 \ g$,$30 \ g$ and $50 \ g$ are $10 \hat{i}$,$10 \hat{j}$ and $10 \hat{k}$,respectively. The velocity of the centre of mass of the three particles is

Consider a two-particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the center of mass through a distance $d$,by what distance should the second particle be moved so as to keep the center of mass at the same position?

Define the centre of mass.

Three circular discs of same material and same thickness of radii $r, 2r$ and $3r$ are placed on a horizontal plane such that their centres lie along a straight line. The radius of the middle disc is $2r$ and it touches the other two discs. The distance of the centre of mass of the system from the centre of the smaller disc is . . . . . . . (in $r$)