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

Let $A = \{a, b, c\}$ and $B = \{1, 2, 3, 4\}$. Then the number of elements in the set $C = \{f : A \rightarrow B \mid 2 \in f(A) \text{ and } f \text{ is not one-one}\}$ is

In a certain office,$72 \%$ of the workers prefer cold drink and $44 \%$ prefer tea. If each of them prefers cold drink or tea and $40$ like both,then the total number of workers in the office is

Each set $X_r$ contains $5$ elements and each set $Y_r$ contains $4$ elements and $\bigcup_{r = 1}^{24} X_r = S = \bigcup_{r = 1}^n Y_r$. If each element of set $S$ belongs to exactly $10$ of the $X_r$'s and to exactly $6$ of the $Y_r$'s,then $n$ is equal to:

Let $A = \{x : x \in R, |x| < 1\}$; $B = \{x : x \in R, |x - 1| \ge 1\}$ and $A \cup B = R - D$,then the set $D$ is

Domain of the function $f(x) = \frac{x - 3}{(x - 1)\sqrt{x^2 - 4}}$ is