Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and λ red, 4 black balls respectively. One of the urns is selected at random and a ball…

Three urns A, B and C contain $\displaystyle 4$ red, $\displaystyle 6$ black; $\displaystyle 5$ red, $\displaystyle 5$ black; and $\displaystyle \lambda$ red, $\displaystyle 4$ 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 $\displaystyle 0.4$ then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola $\displaystyle y^2=\lambda x$ with one vertex at the vertex of the parabola, is