If a set $A$ is such that $A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}$,then the set $A$ could be:

If a set $A$ has $2n + 1$ elements,then how many subsets of $A$ contain at least $n$ elements?

If $A$ and $B$ are two sets such that $n(A) = 70$,$n(B) = 60$,and $n(A \cup B) = 110$,then $n(A \cap B)$ is equal to:

Let $A = \{n \in N : n \text{ is a } 3 \text{-digit number}\}$. Let $B = \{9k + 2 : k \in N\}$ and $C = \{9k + l : k \in N\}$ for some $l$ $(0 < l < 9)$. If the sum of all the elements of the set $A \cap (B \cup C)$ is $274 \times 400$,then $l$ is equal to:

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 $C_{1}$ or chemical $C_{2}$.

$A$ and $B$ are non-singleton sets and $n(A \times B) = 35$. If $B \subset A$,then ${}^{n(A)}C_{n(B)}$ is equal to