If $R = \{ (x,\,y)|x,\,y \in Z,\,{x^2} + {y^2} \le 4\} $ is a relation in $Z$, then domain of $R$ is

Let $A =\{2,3,4,5, \ldots ., 30\}$ and $^{\prime} \simeq ^{\prime}$ be an equivalence relation on $A \times A ,$ defined by $(a, b) \simeq (c, d),$ if and only if $a d=b c .$ Then the number of ordered pairs which satisfy this equivalence relation with ordered pair $(4,3)$ is equal to :

Let $L$ be the set of all straight lines in the Euclidean plane. Two lines ${l_1}$ and ${l_2}$ are said to be related by the relation $R$ iff ${l_1}$ is parallel to ${l_2}$. Then the relation $R$ is

The minimum number of elements that must be added to the relation $R =\{( a , b ),( b , c )$, (b, d) $\}$ on the set $\{a, b, c, d\}$ so that it is an equivalence relation, is $.........$

Let $A = \{1, 2, 3\}, B = \{1, 3, 5\}$. $A$ relation $R:A \to B$ is defined by $R = \{(1, 3), (1, 5), (2, 1)\}$. Then ${R^{ - 1}}$ is defined by

If $A = \left\{ {1,2,3,......m} \right\},$ then total number of reflexive relations that can be defined from $A \to A$ is