Let f(n) = n and g(n) = n^{(1 + sin n)}, where n is a positive integer. Which of the following statements is/are correct?

I. f(n) = O(g(n))

II. f(n) = Ω(g(n))

This question was previously asked in

GATE CS 2015 Official Paper: Shift 3

- Only I
- Only II
- Both I and II
- Neither I nor II

Option 4 : Neither I nor II

Free

IBPS SO IT Officer Mains: Full Mock Test

5486

60 Questions
60 Marks
45 Mins

**Concept: **

Sin function value ranges from -1 to + 1. (-1, 0, 1)

**Explanation:**

**Case 1:** when sin(n) is -1,

g(n) = n^{(1 - 1)} = n^{0} = 1

so, for this case f(n) > g(n) i.e. g(n) = O (f(n))

So, statement 1 is incorrect.

**Case 2:** when sin(n) is +1,

g(n) = n^{(1 + 1)} = n^{2}

so, for this case f(n) < g(n) i.e. f(n) = O(g(n))

but for this, second statement i.e. f(n) = Ω(g(n)) is incorrect.

Both statements are not true for all values of sin(n).

Hence, option 4 is correct answer.
India’s **#1 Learning** Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Trusted by 2,30,67,668+ Students

Start your FREE coaching now >>

Testbook Edu Solutions Pvt. Ltd.

1st & 2nd Floor, Zion Building,

Plot No. 273, Sector 10, Kharghar,

Navi Mumbai - 410210

[email protected]
Plot No. 273, Sector 10, Kharghar,

Navi Mumbai - 410210

Toll Free:1800 833 0800

Office Hours: 10 AM to 7 PM (all 7 days)