A disc of radius r = 20 cm is rotating about its axis with an angular speed of 20 rads^-1. It is gently placed on a horizontal surface which is perfectly frictionless. What is the linear speed of any point on the periphery of the disc? (in m/s)

Since the surface is perfectly frictionless, the disc will not roll on the surface, it will simply keep on rotating at the place where it is placed. 

Now
Linear speed = distance from centre X angular speed
Given, r = 20 cm = 0.2 m and $\mathrm{\omega }$ = 20 rad s^-1.
$\therefore$Linear speed of point on the periphery = r$\mathrm{\omega }$ = 0.2 x 20 = 4 ms^-1.