The induced emf can be produced in a coil by A. moving the coil...

Induced emf is given by Faraday's law

$\left|ε\right| = \dfrac{dϕ}{dt}$

where $ϕ$ is the magnetic flux.

The rate of change of flux through a circuit is defined as emf. The formula for flux is $ϕ = \overset{\to}{B} \cdot \overset{\to}{A}$. In the statements $A \text{ and } B$ 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.