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JEE Advanced Mathematics question

MathematicsPermutations and CombinationsJEE Advanced

Let be a sequence of concentric circles. The th circle has the radius and it has openings. A point P starts travelling on the smallest circle and leaves it at an opening along the normal at the point of opening to reach the next circle . Then it moves on the second circle and leaves it likewise to reach the third circle and so on. The total number of different paths in which the point can come out of the th circle is

Answer: (A)

Solution

On each circle the point makes two independent choices: - the direction of travel along — clockwise or anticlockwise: ways; - the opening through which it leaves : ways.

(The point where it enters is then fixed, because it moves along the

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Question ID VK-109937