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Equilateral triangle inscribed in a parabola with one vertex at its vertex

This type of question, asked 2 times: 24 Jan 2023, 23 Jan 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    24 Jan 2023

    172
    Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and λ\lambda red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn CC is 0.4 then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola y2=λxy^{2}= \lambda x with one vertex at the vertex of the parabola, is
  2. Question 2

    23 Jan 2026 S2

    69
    An equilateral triangle OAB is inscribed in the parabola y2=4xy^{2}= 4x with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having AB as a diameter from the origin is

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