As with any such style questions, the trick is to look at each alternative with a view to knocking out the silly (ie obviously wrong) answers and then worry about the remaining possible options. This question makes distractors a bit of an art form ...
Generally, one can ignore gear. The effect on a certification style of stall demonstration will depend on how the bits sticking out in the wind affect local airflow. If there is a beneficial effect, one might see a knot or two reduction through to a knot or two increase if the flow is not helpful. I'm sure there will be the odd aircraft with a greater effect for some strange reason but I can't bring any to mind just at the moment. If one is looking at other than a certification style of stall, all bets are off to a greater or lesser extent as the boundary conditions for the stall are just too variable .. which is why the certification stall is as it is .. to make things repeatable. So, when thinking about turning stalls, especially at significant bank angles, pilot technique (ie skill) becomes a material factor in the comparison exercise .. which is why the experimental test pilot fraternity is peopled by the higher end of the skill pool.
The main idea of flap is to reduce stall speed (and add drag) so flap is a relevant consideration.
So, let's scratch our heads, alternative by alternative ...
Option (A) in 45 degree bank with power on, the stall occurs at a higher airspeed with gear and flaps down than with gear and flaps up
45 degree bank with power on Same conditions so we can discount that as a distractor .. noting that the conditions set one up for an interesting stall and the possibility of a departure from reasonably controlled flight.
the stall occurs at a higher airspeed with gear and flaps down than with gear and flaps up I don't think so .. one would be expecting a reduction in stall speed with flap down compared to clean. Bin this option.
Option (B ) in power off turns, regardless of the gear and flaps position ,the stall will occur at a higher airspeed with 45 degree of bank than with 30 degree bank
in power off turns, regardless of the gear and flaps position ... distractor
the stall will occur at a higher airspeed with 45 degree of bank than with 30 degree bank Presuming that the turn is a reasonably balanced descending turn, and that we are looking at the same flap configuration, the higher load factor with the higher bank angle will see an increase in stall speed. (Were we looking at a level wind up turn, pilot skill becomes a significant material consideration). (b) is a possible option.
Option (C) in level flight with power off ,a stall would occur at a higher airspeed with gear and flaps down than with gear and flaps up This approximates the usual certification stall although level flight is not feasible as that would require too high a rate of speed reduction approaching the stall.
a stall would occur at a higher airspeed with gear and flaps down than with gear and flaps up
I don't think so .. stall speed would be expected to decrease with flaps extended compared to clean. We can bin this one, too.`
Option (D) in a 60 degree bank with power on or power off, the aeroplane will stall at a lower airspeed with gear and flaps up than with gear and flaps down
in a 60 degree bank with power on or power off Distractor, noting that a stall in such flight conditions might set one up for a spin without too much trouble, especially power on ...
the aeroplane will stall at a lower airspeed with gear and flaps up than with gear and flaps down I don't think so .. again, presuming we are comparing bank/power apples with apples, we would expect the lower stall speed with flaps extended compared to clean. Bin this one, too.
Guess that leaves us with option (B ) ? .. unless all the distractor mumbo jumbo in the question got to me ...
