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

(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.

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Last Updated : 13 Nov, 2017

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

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