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Explanation:

P and Q do not lie within the intersection of the two circles.

So they lie on the circumferences or outside the circumferences.

Case 1: If they lie on the circumferences, then ΔAPQ forms an equilateral triangle.
So, m ∠AQP = 60°

Case 2: From the diagram, if they lie outside the circumferences,
m ∠AQ'P' < 60°
Also, m ∠AQP would be 0° if A, Q and P were collinear.
But as P and Q cut each other in two distinct points, A, Q and P cannot be collinear.
∴ m ∠AQP > 0°

∴ The value, m ∠AQP lies between 0° and 60°

Hence, option (c).

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