JEE Main 2014 · 11 Apr · Shift 1 · Mathematics Q72

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For the curve $y=3\sin\theta\cos\theta$ , $x=e^\theta\sin\theta$ , $0\le\theta\le\pi$ , the tangent is parallel to $x$ -axis when $\theta$ is :

\dfrac{3\pi}4

\dfrac\pi2

\dfrac\pi4

\dfrac\pi6

Answer and worked solution

Official answer: C

$\dfrac{dy}{d\theta}=3\cos2\theta=0$ at $\theta=\frac\pi4,\frac{3\pi}4$ . Also $\dfrac{dx}{d\theta}=e^\theta(\sin\theta+\cos\theta)$ is non-zero at $\frac\pi4$ but zero at $\frac{3\pi}4$ . So the tangent is horizontal at $\theta=\dfrac\pi4$ .

Topics:Tangents and normals Parametric differentiation

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JEE Main 2014 · 11 Apr · Shift 1, Mathematics question 72