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 group of $70$ people,$37$ like coffee,$52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

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:

Which of the following statements is false for the sets $A, B$ and $C,$ where
$A = \{x \mid x \text{ is a letter of the word } 'BOWL'\}$
$B = \{x \mid x \text{ is a letter of the word } 'ELBOW'\}$
$C = \{x \mid x \text{ is a letter of the word } 'BELLOW'\}$

If $A = \{x, y\}$,then the power set of $A$ is

If $aN = \{ ax : x \in N \}$,then the set $3N \cap 7N$ is equal to .....$N$.