Match the items in column $$I$$ and $$II$$

List $$I$$
$$P.$$ Higher kinematic pair
$$Q.$$ Lower kinematic pair
$$R.$$ Quick return mechanism
$$S.$$ Mobility of a linkage

List $$II$$
$$1.$$ Grubler's equation
$$2.$$ Line contact
$$3.$$ Euler's equation
$$4.$$ planar
$$5.$$ Shaper
$$6.$$ Surface contact

A planetary gear train has four gears and one carrier. Angular velocities of the gears are $${\omega _1},{\omega _2},{\omega _3},$$ and $${\omega _4}$$ respectively. The carrier rotates with angular velocity $${\omega _5}.$$

What is the relation between the angular velocities of Gear $$1$$ and Gear $$4$$?

The number of inversions for a slider crank mechanism is

For a four bar linkage in Toggle position, the value of mechanical advantage is