Coercivity of a ferromagnetic material? I understand that coercivity is the field/force required to demagnetize/magnetize a ferromagnetic material.
What if we had two opposite magnetic fields of different strengths values H acting on the same ferromagnet what would happen? 
H1 = 50 Oe
H2 = 10 Oe
The coercivity of the material is 0.5 Oe, what would happen? Will it stay magnetized to the stronger field(H1)? Or magnetization = 0?
 A: Magnetic field is additive, so if I understand you correctly your magnet would be in 40 Oe field in direction of H1. As this is more than coercivity magnet will be magnetized by that effective field. 
As a sidenote: in ferromagnetic materials it's not that easy to obtain zero magnetization. In zero field you would have spontaneous magnetization. But this can be (almost) done by applying alternating field with amplitude lowering over time. See degaussing on Wikipedia for example (section about CRTs to be precise). Magnetization is not entirely removed, but randomized, and it's amplitude vastly diminished.
EDIT:
If you have no magnetization and you don't exceed coercive field you will have magnetization which is not permanent, and will vanish soon after you take your field away. If you exceed coercivity you will get permanent magnetization which will decrease slightly if you take field away. Now if you change direction of field to opposite you will get decreasing magnetization with growing field. At field strength equal to coercivity you will get zero magnetization, and then direction of your magnetization will switch if you keep increasing field any further. Look up histeresis curve. Here you have it really nicely detailed. In your example all of this is unimportant as field strength is much higher than coercivity so sample will magnetize in direction of stronger field no matter what.
