If algorithm A and another algorithm B take log2(n) and √n microseconds, respectively, to solve a problem, then the largest size n of a problem these algorithms can solve. respectively. in one second are_____ and _____.  

This question was previously asked in
UGC NET Computer Science (Paper 2) 2020 Official Paper
View all UGC NET Papers >
  1. \({2^{{{10}^6}}}and\;{10^6}\)
  2. \({2^{{{10}^6}}}and\;{10^{{12}}}\)
  3. \({2^{{{10}^6}}}and\;{6.10^6}\)
  4. \({2^{{{10}^6}}}and\;{6.10^{12}}\)

Answer (Detailed Solution Below)

Option 2 : \({2^{{{10}^6}}}and\;{10^{{12}}}\)
Free
UGC NET Paper 1: Held on 21st August 2024 Shift 1
8.8 K Users
50 Questions 100 Marks 60 Mins

Detailed Solution

Download Solution PDF

The correct answer is option 2.
Explanation:

A microsecond is 10-6 seconds. Hence, one second =10microseconds

One hour=60x60x106= 3.6x10microseconds

One month=2.592x1012microseconds

One century=3.1104x1015microseconds

f(n)=logn in this case,the largest value n such that logn <=106.

We rewrite as, 2logn <= 2(10)^6 

thus, 21000000 = (210)100000 = (103)100000 = 10300000

Hence, log2(n) and √n, In one second

\({2^{{{10}^6}}}and\;{10^{{12}}}\) the value will be 106 and 106

Hence the correct answer is option 2.

Latest UGC NET Updates

Last updated on Jun 6, 2025

-> The UGC NET Exam Schedule 2025 for June has been released on its official website.

-> The UGC NET Application Correction Window 2025 is available from 14th May to 15th May 2025.

-> The UGC NET 2025 online application form submission closed on 12th May 2025.

-> The June 2025 Exam will be conducted from 21st June to 30th June 2025

-> The UGC-NET exam takes place for 85 subjects, to determine the eligibility for 'Junior Research Fellowship’ and ‘Assistant Professor’ posts, as well as for PhD. admissions.

-> The exam is conducted bi-annually - in June and December cycles.

-> The exam comprises two papers - Paper I and Paper II. Paper I consists of 50 questions and Paper II consists of 100 questions. 

-> The candidates who are preparing for the exam can check the UGC NET Previous Year Papers and UGC NET Test Series to boost their preparations.

More Asymptotic Notations Questions

More Asymptotic Worst Case Time and Time Complexity Questions

Get Free Access Now
Hot Links: teen patti master 2025 teen patti online teen patti pro teen patti wala game teen patti sequence