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MCQMediumJEE Main 2023 · 31 January, Shift 1Conic Sections (Parabola, Ellipse, Hyperbola)

Mathematics Question from JEE Main 2023 · 31 January, Shift 1

Let y=f(x)y = f(x) represent a parabola with focus (−12,0)\left( -\frac{1}{2}, 0 \right) and directrix y=−12y = -\frac{1}{2}.

Then S={x∈R:tan⁡−1(f(x))+sin⁡−1(f(x)+1)=π2}S = \left\{ x \in \mathbb{R} : \tan^{-1} \left( \sqrt{f(x)} \right) + \sin^{-1} \left( \sqrt{f(x) + 1} \right) = \frac{\pi}{2} \right\} contains:

  • A

    Exactly two elements

  • B

    Exactly one element

  • C

    An infinite set

  • D

    An empty set

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