If $n(A) = 4$,$n(B) = 3$,and $n(A \times B \times C) = 24$,then $n(C) = $

Domain and range of $f(x) = \frac{|x - 3|}{x - 3}$ are respectively

Consider the two sets:
$A = \{m \in R : \text{both the roots of } x^{2} - (m+1)x + m+4 = 0 \text{ are real}\}$ and $B = [-3, 5)$.
Which of the following is not true?

Let $A = \{1, 2, 3\}$. The total number of distinct relations that can be defined over $A$ is

If $A = \{1, 2, 3, 4, ..., 100\}$ and $B = \{51, 52, 53, ..., 180\}$,then the number of elements in $(A \times B) \cap (B \times A)$ is:

Let $X = \{ 1, 2, 3, 4, 5 \}$ and $Y = \{ 1, 3, 5, 7, 9 \}$. Which of the following is/are relations from $X$ to $Y$?