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Question

All the arcs in the following diagram are semi-circles. This diagram shows two paths connecting A to B. Path I is the single large semi-circle and Path II consists of the chain of small semi-circles.
613568_928588cdcdf5471ca45c1541e02eb385.png

A
Path I is longer than Path II
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B
Path I of the same length of Path II
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C
Path I is shorter than Path II
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D
Path I is of the same length as Path II. Only if the number of semi circles is not more than 4
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Solution

The correct option is A Path I is longer than Path II
Let the length of AB be d

So the radius of larger semi circle is d2 and the radius of smaller semi circle is d8

So the length of AB through path 1 is π×d2=πd2

So the length of AB through path 2 is 4×π×d8=πd2

So the both paths are of same length

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