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 :
The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is ____________.
A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let $$\mathrm{X}$$ be the number of white balls, among the drawn balls. If $$\sigma^{2}$$ is the variance of $$\mathrm{X}$$, then $$100 \sigma^{2}$$ is equal to ________.
The probability distribution of X is :
| X | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| P(X) | $${{1 - d} \over 4}$$ | $${{1 + 2d} \over 4}$$ | $${{1 - 4d} \over 4}$$ | $${{1 + 3d} \over 4}$$ |
For the minimum possible value of d, sixty times the mean of X is equal to _______________.