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Engineering

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 C 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

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