Four boxes $A, B, C$ and $D$ contain 5000, 3000, 2000 and 1000 fuses respectively. The percentages of defective fuses in these boxes are $3 \%, 2 \%, 1 \%$ and $0.5 \%$ respectively. If a fuse selected at random from one of the boxes is found to be defective, then the probability that it has come from box $D$ is

A die is thrown thrice. If getting 1 or 6 in a single throw is considered as success, then the variance of the number of successes is

In a hospital, on an average if there are 35 births in a weak, then the probability that there will be less than 3 births in a day, is

Let $A(2,1)$ be a point and equation of the straight line $L$ be $x-y=0$. Let $a$ and $b$ respectively represent the distances from a variable point $P(\alpha, \beta)$ to $A$ and to the line $L$. If $C$ is distance of the point $A$ from origin such that $a=b c$, then locus of $P$ is