Let $A = \{n \in N \mid n^{2} \leq n + 10,000\}$,$B = \{3k + 1 \mid k \in N\}$,and $C = \{2k \mid k \in N\}$. Then the sum of all the elements of the set $A \cap (B - C)$ is equal to $.....$

If a number is chosen at random from the first $200$ positive integers,what is the probability that it is divisible by $6$ or $8$?

The smallest set $A$ such that $A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}$ is

The lengths of the sides and the diagonal of an isosceles trapezium form a two-element set $\{a, b\}$. If $a > b$,then $a / b$ equals

Suppose $A_1, A_2, A_3, \dots, A_{30}$ are $30$ sets each having $5$ elements and $B_1, B_2, \dots, B_n$ are $n$ sets each with $3$ elements. Let $\bigcup_{i=1}^{30} A_i = \bigcup_{j=1}^n B_j = S$ and each element of $S$ belongs to exactly $10$ of the $A_i$'s and exactly $9$ of the $B_j$'s. Then $n$ is equal to:

In a survey,it was found that $21$ people liked product $A$,$26$ liked product $B$,and $29$ liked product $C$. If $14$ people liked products $A$ and $B$,$12$ people liked products $C$ and $A$,$14$ people liked products $B$ and $C$,and $8$ liked all three products,find how many people liked product $C$ only.