A motorjet is a very early type of jet engine where intake air passes through a compressor driven by a separate piston engine, and is then mixed with fuel and burned to provide thrust. They were used in a handful of designs around the time of World War II, but fell out of favour when gas turbine metallurgy had advanced to the point where it was feasible to drive the engine compressor from a turbine in the exhaust stream without having to rebuild the engine every few flights; all else being equal, a motorjet, requiring an entire second engine to drive the compressor, is heavier, and, thus, has a lower thrust-to-mass ratio than a turbojet or turbofan. Are there any situations where a motorjet would still be a better choice than a turbojet or turbofan?
I can think of a few maybes:
Aircraft using fuel that produces refractory oxides when burned (such as boron-containing fuels and most organometallics), or operating in air heavily contaminated with particles of same (such as volcanic ash clouds), as these are very hard on turbines unless the exhaust gas temperature (EGT) remains high enough to vapourise these oxides all the way out the tailpipe; a motorjet has no turbine blades in the exhaust stream to suffer ill effects from this (unlike a turbojet or turbofan), does not need an onboard supply of oxidiser (unlike a rocket), and produces reasonable thrust even at zero airspeed (unlike a ramjet).
Aircraft with very severe length restrictions, as a turbojet or turbofan's compressor(s) and turbine(s) all have to be in line with one another, whereas a motorjet's compressor motor could be stacked vertically above the compressor and combustion chamber.
VTOL aircraft, where the torque and gyroscopic effects from all that heavy, rapidly-spinning turbomachinery can cause control problems while hovering or moving at very low speed (due to the control authority of aerodynamic control surfaces being very low at very low airspeeds, and nil at zero airspeed), as pointed out in this comment by Peter Kämpf on an answer to one of my earlier questions.