MCQ_SINGLE

Let $A = {1, 2, 3, 4, 5}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $4x \le 5y$. Let $m$ be the number of elements in $R$ and $n$ be the minimum number of elements from $A \times A$ that are required to be added to $R$ to make it a symmetric relation. Then $m + n$ is equal to :

MCQ_SINGLE

Let $R_1$ and $R_2$ be two relations defined on $R$ by $aR_1b \Leftrightarrow ab \ge 0$ and $aR_2b \Leftrightarrow a \ge b$. Then,

MCQ_SINGLE

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

NUMERICAL

Let A = {n $ \in $ N: n is a 3-digit number} B = {9k + 2: k $ \in $ N} and C = {9k + $l$: k $ \in $ N} for some $l ( 0 < l < 9)$ If the sum of all the elements of the set A $ \cap $ (B $ \cup $ C) is 274 $ \times $ 400, then $l$ is equal to ________.

NUMERICAL

Let $A=\{1,2,3,4\}$ and $R=\{(1,2),(2,3),(1,4)\}$ be a relation on $\mathrm{A}$. Let $\mathrm{S}$ be the equivalence relation on $\mathrm{A}$ such that $R \subset S$ and the number of elements in $\mathrm{S}$ is $\mathrm{n}$. Then, the minimum value of $n$ is __________.

View All Questions