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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:

  1. $\log_{2}n$, $\frac{100}{n}$, $10$, $\sqrt{n}$, $n$
  2. $\frac{100}{n}$, $10$, $\log_{2}n$, $\sqrt{n}$, $n$
  3. $10$, $\frac{100}{n}$, $\sqrt{n}$, $\log_{2}n$, $n$
  4. $\frac{100}{n}$, $\log_{2}n$, $10$, $\sqrt{n}$, $n$
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12 Answers

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

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 

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
Answer:

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