###### Digital-Logic-Design

October 12, 2023###### GATE 2017 [Set-1]

October 12, 2023# GATE 2017 [Set-1]

Question 4 |

Consider the following functions from positives integers to real numbers

The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:

Question 4 Explanation:

In this problem, they are expecting to find us “increasing order of asymptotic complexity”.

Step-1: Take n=2048 or 2

Step-2: Divide functions into 2 ways

1. Polynomial functions

2. Exponential functions

Step-3: The above functions are belongs to polynomial. So, simply substitute the value of n,

First compare with constant values.

→ 100 / 2048 = 0.048828125

→ 10 > 100/ 2048

→ log

→ √n = 45.25483399593904156165403917471

→ n = 2048

So, Option B is correct

Step-1: Take n=2048 or 2

^{11}(Always take n is very big number)Step-2: Divide functions into 2 ways

1. Polynomial functions

2. Exponential functions

Step-3: The above functions are belongs to polynomial. So, simply substitute the value of n,

First compare with constant values.

→ 100 / 2048 = 0.048828125

→ 10 > 100/ 2048

→ log

_{2}2048 =11→ √n = 45.25483399593904156165403917471

→ n = 2048

So, Option B is correct

Correct Answer: B

Question 4 Explanation:

In this problem, they are expecting to find us “increasing order of asymptotic complexity”.

Step-1: Take n=2048 or 2

Step-2: Divide functions into 2 ways

1. Polynomial functions

2. Exponential functions

Step-3: The above functions are belongs to polynomial. So, simply substitute the value of n,

First compare with constant values.

→ 100 / 2048 = 0.048828125

→ 10 > 100/ 2048

→ log

→ √n = 45.25483399593904156165403917471

→ n = 2048

So, Option B is correct

Step-1: Take n=2048 or 2

^{11}(Always take n is very big number)Step-2: Divide functions into 2 ways

1. Polynomial functions

2. Exponential functions

Step-3: The above functions are belongs to polynomial. So, simply substitute the value of n,

First compare with constant values.

→ 100 / 2048 = 0.048828125

→ 10 > 100/ 2048

→ log

_{2}2048 =11→ √n = 45.25483399593904156165403917471

→ n = 2048

So, Option B is correct

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