Acoil formed by wrapping 50 turns of wire in the shape of a square is positioned in a magnetic field so that the normal to the plane of the coil makes an angle of 30.0 ? with the direction of the field. when the magnetic field is increased uniformly from 200 ? t to 600 ? t in 0.400 s, an emf of magnitude of 80.0 mv is induced in the coil. what is the total length of the wire?

The induced voltage is N(-dΦ/dt)  where N=50 and flux is Φ=BAcos(θ).  B is the field and A is the area.  The trick is to see that because the loop is a square with side length L, that the area is L^2.  For your magnetic flux density values I'm seeing "200 ?t" and 600 ?t"  Am I right in thinking these are microTesla, uT?  I will assume so but if it's something else you'll have to find the answer again So dB/dt = (600e-6-200e-6)/0.4=1e-3.  Now,
80mV=(50)(1e-3)(L^2)cos(30)
L = 1.359m
Thus the perimeter of the square is 4(1.359m) = 5.437m
And the total length is (50)(5.437m) = 271.85m

Answer (d) the universe had cooled enough for atoms to combine, protons and neutrons were too far apart to form nuclei;

The best answer i can think of is b