When 3 dice are thrown at a time, the sum of the numbers appeared on 3 dice were found to be 15 . Then, the probability that the number 5 does not appear on any one of the dice is

If the probability distribution of a random variable $X$ is given by

$$ \begin{array}{|c|c|c|c|c|c|c|} \hline X=x & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline P(X=x) & 0 & k & 2 k & 5 k^2 & 2 k^2 & 3 k \\ \hline \end{array} $$

then the mean of $X$ is

The probability of getting a success in a trail is five times that of a failure. The probability of getting atmost one success in 5 trails, is

$B(2,3), C(5,-2), D(1,-1)$ are three points. If $A$ is a variable point such that the area of the quadrilateral $A B C D$ is 10 sq. units, then the locus of $A$ is