Induced emf is given by Faraday's law

where is the magnetic flux.

The rate of change of flux through a circuit is defined as emf. The formula for flux is . In the statements A&B given in the question, the magnetic flux in the coil in uniform magnetic field does not change. So, no emf is induced.

But in statement C, the angle between the area vector and the magnetic field continuously changes hence, an emf is generated. In statement D, the area is changing in unit time so magnetic flux will change and an emf is generated.