The number of elements in the relation $R = \{(x, y) : 4x^{2} + y^{2} < 52, x, y \in Z\}$ is

The solution set of $x \equiv 3 \pmod{7}$,where $x \in \mathbb{Z}$,is:

Let the relation $R$ be defined on the set of natural numbers $N$ by $a R b$ if $3 a+2 b=27$. Then $R$ is:

If $A$ is the set of even natural numbers less than $8$ and $B$ is the set of prime numbers less than $7$,then the number of relations from $A$ to $B$ is

Let $A = \{1, 2, 3\}$ and $B = \{1, 3, 5\}$. If a relation $R$ from $A$ to $B$ is defined as $R = \{(1, 3), (2, 5), (3, 3)\}$,then find the inverse relation ${R^{ - 1}}$.

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