Official PYQ · 2014Set 1 · Q6Calculus: Limits, Continuity, DifferentiabilityMCQ1 mark

GATE CS 2014 Set 1 Q6 — Calculus: Limits, Continuity, Differentiability

Let the function

$f(\theta) = \begin{vmatrix} \sin\theta & \cos\theta & \tan\theta \\ \sin(\frac{\pi}{6}) & \cos(\frac{\pi}{6}) & \tan(\frac{\pi}{6}) & \\ \sin(\frac{\pi}{3}) & \cos(\frac{\pi}{3}) & \tan(\frac{\pi}{3}) \end{vmatrix}$

where

$\theta \in \left[ \frac{\pi}{6},\frac{\pi}{3} \right]$ and $f'(\theta)$ denote the derivative of $f$ with respect to $\theta$ . Which of the following statements is/are TRUE?

There exists $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta) = 0$
There exists $\theta \in (\frac{\pi}{6},\frac{\pi}{3})$ such that $f'(\theta)\neq 0$

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Answer: C

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Published 10 Oct 2026

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