This question checks whether you know what d'Alembert's paradox actually says, not just its name. It is a classical result from ideal (inviscid, irrotational) flow theory, so look at each option with that in mind.
- Deviation of drag from $D \propto v^2$ at very low speeds: at very low speeds (creeping/Stokes flow), drag actually goes as \(D \propto v\), not \(v^2\), but this is a viscous, low Reynolds number effect and has no connection to potential flow theory.
- Deviation of drag from $D \propto v^2$ at high subsonic speeds: at high subsonic speeds the drag rises faster than \(v^2\) because of compressibility, again a real-fluid effect, not what d'Alembert described.
- Prediction of zero drag by potential flow theory: solving the flow around a body using potential theory (no viscosity, no vorticity) gives a symmetric pressure distribution on the front and back of the body. The pressure forces on the front exactly cancel the pressure forces on the back, so the net drag works out to zero. Every real body still has drag, so this "zero drag" result is the paradox.
- Presence of shocks in transonic flows: shocks are a compressible flow phenomenon and do not enter the incompressible potential flow argument at all.
Only option (C) matches the actual statement of the paradox: an inviscid, irrotational flow model predicts zero drag on any closed body, even though real bodies always experience drag.
Let's summarize:
- Potential flow theory has no viscosity, so it cannot generate the friction or the pressure asymmetry (from boundary layer separation) that real drag needs.
- The mismatch between "theory says zero drag" and "experiment always shows drag" is exactly d'Alembert's paradox.
So the correct option is (C), prediction of zero drag by potential flow theory.