54 votes 54 votes Consider the following functions from positive integers to real numbers: $10$, $\sqrt{n}$, $n$, $\log_{2}n$, $\frac{100}{n}$. The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is: $\log_{2}n$, $\frac{100}{n}$, $10$, $\sqrt{n}$, $n$ $\frac{100}{n}$, $10$, $\log_{2}n$, $\sqrt{n}$, $n$ $10$, $\frac{100}{n}$, $\sqrt{n}$, $\log_{2}n$, $n$ $\frac{100}{n}$, $\log_{2}n$, $10$, $\sqrt{n}$, $n$ Algorithms gatecse-2017-set1 algorithms asymptotic-notation normal + – khushtak asked Feb 14, 2017 edited Jun 24, 2018 by Shikha Mallick khushtak 17.6k views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Arjun commented Feb 14, 2017 reply Follow Share 1 is also added: https://gateoverflow.in/tag/gate2017-1?start=30 1 votes 1 votes Abhijit Sen commented Feb 15, 2017 reply Follow Share Hi, if we take n=21024 , then logn gives me 1024, which is greater than 10. So why D won't be the answer? 0 votes 0 votes Hira Thakur commented Jan 3 i edited by Hira Thakur Jan 3 reply Follow Share The same type of concept asked inGATE IT 2008 | Question: 10GATE CSE 2011 | Question: 37,GATE CSE 2021 Set 1 | Question: 3 0 votes 0 votes Jyotiprakash Chanda commented Feb 6 reply Follow Share If 1024 is greater than 10 so logn is greater than 10 which is option B is correct. 0 votes 0 votes Please log in or register to add a comment.
9 votes 9 votes 100/n grows inversely with n so for very large values of n, it will become close to zero. 10 IS CONSTANT. 100/n<10 among rest of choices it is very clear that log n < sqrt(n)<n thus 100/n<10< log n < sqrt(n)<n CHOICE B sushmita answered Aug 28, 2017 sushmita comment Share Follow See all 0 reply Please log in or register to add a comment.
6 votes 6 votes O(100/N), O(10), O(logN), O(N1/2), O(N) sandeep007734 answered Feb 13, 2017 sandeep007734 comment Share Follow See all 0 reply Please log in or register to add a comment.
6 votes 6 votes let take a very large N value of 21024 Now putting this in the respective terms we get B is the correct answer here NOTE: More editing coming up Aboveallplayer answered Feb 14, 2017 Aboveallplayer comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes Easily comparison by taking a log of all the value and put n equals to the large value. We get option B is correct order Raj Kumar 7 answered Dec 24, 2017 Raj Kumar 7 comment Share Follow See all 0 reply Please log in or register to add a comment.