The number of degrees of freedom in a planner mechanism having $$n$$ links and $$j$$ simple hinge joints is

A single degree of freedom mass-spring - viscous damper system with mass $$m,$$ spring constant $$k$$ and viscous damping coefficient $$q$$ is critically damped. The correct relation among $$m, k$$ and $$q$$ is

The number of degrees of freedom of the planetary gear train shown in the figure is

A wheel of radius r rolls without slipping on a horizontal surface shown below. If the velocity of point P is 10m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) is ______