(a) False. This is because if steel and rubber wires of same length and area of cross-section are subjected to same deforming force, then the extension produced in steel is less than the extension produced in rubber.
So YS>YR. In other words, for producing same strain in steel and rubber, more stress is required in case of steel.
(b) True. The reason is that when a coil spring is stretched, there is neither a change in the length of the coil (i.e., length of the wire forming the coil spring) nor a change in its volume. Since the change takes place in the shape of the coil spring, its stretching is determined by its shear modulus.