Mathematics Question from JEE Main 2023 · 24 January, Shift 2

The urns $A$, $B$, and $C$ contain $4$ red, $6$ black; $5$ red, $5$ black, and $\lambda$ 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 $y^2 = \lambda x$ with one vertex at the vertex of the parabola, is: