A rectangular, a square, a circular and an elliptical loop, all in the $(x-y)$ plane, are moving out of a uniform magnetic field with a constant velocity, $\vec{v}=v\hat{i}$. The magnetic field is directed along the negative $z$ axis. The induced emf will not remain constant for:

Induced emf $e=Bvl$, where $l$ is the effective length of the conductor moving perpendicular to the magnetic field.For a rectangular or square loop moving out, the effective length $l$ (width) remains constant as it exits the field. Thus, emf is constant.For circular and elliptical loops, the effective width $l$ varies as different segments exit the field (it starts small, increases to the diameter, and decreases again).Thus, the induced emf is not constant for circular and elliptical loops.