Question

Three 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

Answer 1

The correct answer is 432

P(RC​)=P(A)P(AR​)+P(B)P(BR​)+P(C)P(CR​)P(C)P(CR​)​
0.4=31​×104​+31​×105​+31​(λ+4)λ​31​×(λ+4)λ​​
⇒λ=6

tan30∘=3t=23​t2
3​1​=t2​
t=23​
(23​t2,3t)=(18,63​)
ℓ2=182+(63​)2
=324+108
=432