GATE CS 2026 Set 2 — Question 24
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Question
Consider the following functions, where is a positive integer.Which one of the following options lists the functions in increasing order of asymptotic growth rate?Note: Assume the base of log to be 2.
Correct answer
(A) log(n), n^(1/3), 2^(log(n)), log(n!)
Solution
We analyze the asymptotic growth of each function:
This corresponds to Option (A).
1.: Logarithmic growth.
2.: Polynomial growth (power ). We know that any polylogarithmic function grows slower than any polynomial function with positive power. Thus, .
3.: Assuming base 2, . This is linear growth. Since , .
4.: Using Stirling's approximation, . This grows faster than linear ().
The increasing order is:This corresponds to Option (A).
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