If $A$ and $B$ are two sets,then $A \cap (A \cup B)'$ is equal to

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 certain class,$72 \%$ of the students took Biology and $44 \%$ took Mathematics. If each student took at least one of Biology or Mathematics and $40$ students took both of these subjects,the total number of students in the class is:

In a class of $100$ students,$55$ students have passed in Mathematics and $67$ students have passed in Physics. Then the number of students who have passed in Physics only is

If $(1, 3), (2, 5)$ and $(3, 3)$ are three elements of $A \times B$ and the total number of elements in $A \times B$ is $6$,then the remaining elements of $A \times B$ are

If the sets $A$ and $B$ are defined as $A = \{ (x, y) : y = e^x, x \in R \}$ and $B = \{ (x, y) : y = x, x \in R \}$,then