Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

GATE | GATE-CS-2014-(Set-1) | Question 16

  • Last Updated : 13 Nov, 2017

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

Answer: (C)

Explanation: In the given question,\theta ranges from \pi /6 to \pi /3.
When \theta=\pi /6, the value of the function is 0, since Rows 1 and 2 are the same.
When \theta=\pi /3, the value of the function is 0, since Rows 1 and 3 are the same.
Therefore, f(\pi /6) = f(\pi /3) =0
The given function is continuous and differentiable in the given range since it is a trigonometric function.
Then According to the Mean Value Theorem,
There exists a value c of such that f'(c)=0. So the first statement is true.
Also there may also exist a value c, such that f'(c)\neq 0. This is because the function is not a constant function, i.e. all values in the range are not equal to c.
So the second statement is also true.
Therefore the correct option is C.

Quiz of this Question

My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!