This question checks whether you can tell apart the two Mach numbers used to describe compressibility effects on a wing, and what each one physically means.
- Critical Mach number is the minimum freestream Mach number for which sonic condition is attained somewhere over the wing: Picture the pressure distribution over a wing at increasing freestream Mach number $M_\infty$. As $M_\infty$ rises, the peak suction pressure on the upper surface (where flow speed is highest) also rises. The critical Mach number $M_{cr}$ is, by definition, the smallest $M_\infty$ at which this local peak velocity first touches $M=1$. This matches the option exactly, so it is correct.
- Drag divergence Mach number is always higher than the critical Mach number: Just past $M_{cr}$, only a thin sliver of supersonic flow exists on the wing and the drag rise is mild. As $M_\infty$ keeps climbing beyond $M_{cr}$, this supersonic zone widens and eventually ends in a shock strong enough to separate the boundary layer, which is what actually drives the steep drag rise called $M_{dd}$. Since this growth needs $M_\infty$ above $M_{cr}$, we always have $M_{dd} > M_{cr}$, so the statement is correct.
- Drag divergence Mach number is the local Mach number over the wing at which the drag increases drastically: $M_{dd}$ is reported as a freestream flight or tunnel Mach number, not the (much higher) local Mach number that exists inside the supersonic pocket on the wing surface. Mixing up local and freestream values makes this statement wrong.
- Critical Mach number is independent of the angle of attack: Changing the angle of attack changes the pressure (and hence velocity) distribution over the wing, in particular the suction peak near the leading edge. A higher angle of attack pushes the local peak velocity higher for the same $M_\infty$, so sonic flow is reached at a lower $M_\infty$. $M_{cr}$ therefore drops as angle of attack increases, so it is not independent of it, and this statement is wrong.
So the true statements are the first two, options A and B.
Let's summarize:
- $M_{cr}$ is where sonic flow first appears locally on the wing; $M_{dd}$ is a higher, later freestream Mach number where the drag shoots up because of shock-induced separation.
- Both $M_{cr}$ and $M_{dd}$ change with angle of attack because they depend on the local pressure/velocity distribution, which the angle of attack controls.
The correct options are A and B.