GATE | GATE-CS-2015 (Set 3) | Question 65

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))  

(A) Only I
(B) Only II
(C) Both I and II
(D) Neither I nor II


Answer: (D)

Explanation: The value of sine function varies from -1 to 1.
For sin = -1 or any other negative value, I becomes false.
For sin = 1 or any other positive value, II becomes false.


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