Skip to content
GATEiit

GATE CSE 2026 Session 2 Q24: Order n^(1/3), log n, log(n!), 2^(log n) by growth rate

Question

Consider the following functions, where nn is a positive integer.

n1/3,log⁡(n),log⁡(n!),2log⁡(n)n^{1/3}, \quad \log(n), \quad \log(n!), \quad 2^{\log(n)}

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.

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 1/3 mark in GATE.
Show answer and explanation

Answer: A (official GATE 2026 final answer key)

Concept used: Simplify each function: 2log⁡2n=n2^{\log_2 n} = n and log⁡(n!)=Θ(nlog⁡n)\log(n!) = \Theta(n \log n).

First step: Rewrite 2log⁡n2^{\log n} as nn and use Stirling's approximation for log⁡(n!)\log(n!).

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

WhatsAppDownload image

Source: official GATE 2026 Session 2 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

More Algorithms PYQs

PracticePractise Algorithms questions →Full paperAll GATE CSE 2026 Session 2 questions →