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GATE 2025 EC – Question 4

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after ‘Iteration $n$’ is:

Note: The figures shown are representative.

Diagram for GATE 2025 EC question 4
  1. $\left(\frac{5}{3}\right)^{n/2}$
  2. $\left(\frac{5}{3}\right)^{n}$
  3. $\left(\frac{5}{3}\right)^{2n}$
  4. $\left(\frac{5}{3}\right)^{n(2n-1)}$

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Correct answer: (B) $\left(\frac{5}{3}\right)^{n}$

Explanation

Iteration 0 has one segment of length 1. Each iteration replaces every segment by 5 segments that are 1/3 as long. After iteration $n$ there are $5^n$ segments, each of length $(1/3)^n$, so the total length is $5^n/3^n=(5/3)^n$.