Sets $A$ and $B$ have $3$ and $6$ elements respectively. What can be the minimum number of elements in $A \cup B$?

If $n(A) = 3$,$n(B) = 6$ and $A \subseteq B$. Then the number of elements in $A \cup B$ is equal to

$205$ students take an examination,of whom $105$ pass in English,$70$ students pass in Mathematics,and $30$ students pass in both. How many students fail in both subjects?

The probability of failing in Physics is $20\%$,and the probability of failing in Mathematics is $10\%$. What is the probability of failing in at least one subject (in $\%$)?

There are $200$ individuals with a skin disorder. $120$ had been exposed to the chemical $C_{1}$,$50$ to chemical $C_{2}$,and $30$ to both the chemicals $C_{1}$ and $C_{2}$. Find the number of individuals exposed to chemical $C_{1}$ but not chemical $C_{2}$.

$A$ group of $40$ students appeared in an examination of $3$ subjects - Mathematics,Physics,and Chemistry. It was found that all students passed in at least one of the subjects. $20$ students passed in Mathematics,$25$ students passed in Physics,and $16$ students passed in Chemistry. At most $11$ students passed in both Mathematics and Physics,at most $15$ students passed in both Physics and Chemistry,and at most $15$ students passed in both Mathematics and Chemistry. The maximum number of students who passed in all the three subjects is . . . . . . .