GATE EC 2025 Set 1 — Question 4
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Question
The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after ‘Iteration ' is:
Note: The figures shown are representative.
Note: The figures shown are representative.
Correct answer
(B) ((5)/(3))ⁿ
Solution
Let be the total length of the curve after Iteration .Iteration 0:
Length = 1Iteration 1:
The initial segment of length 1 is replaced by 5 segments, each of length .
So, .Iteration 2:
Each segment of length from Iteration 1 is replaced by 5 segments, each of length of the previous segment's length. So, each new segment has length .
The number of segments becomes .
So, .From the pattern, for Iteration , the total length will be .Therefore, the missing word in Group-II is Appreciate.The final answer is .
Length = 1Iteration 1:
The initial segment of length 1 is replaced by 5 segments, each of length .
So, .Iteration 2:
Each segment of length from Iteration 1 is replaced by 5 segments, each of length of the previous segment's length. So, each new segment has length .
The number of segments becomes .
So, .From the pattern, for Iteration , the total length will be .Therefore, the missing word in Group-II is Appreciate.The final answer is .
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