Sets and Relations

107 questions · Mathematics · JEE Main

Sets and Relations

107 questions · Mathematics · JEE Main

Let A be the set of all functions $f : Z \to Z$ and R be a relation on A such that $R = {(f, g) : f (0) = g (1)$ and $f (1) = g (0)}$ . Then R is :2025 · 2 Apr · Shift 1 · Q41 · MCQ
Let $A = {1, 2, 3, \dots ., 100}$ and $R$ be a relation on $A$ such that $R = {(a, b) : a = 2 b + 1}$ . Let $(a_{1}$ , $a_{2}), (a_{2}, a_{3}), (a_{3}, a_{4}), \dots ., (a_{k}, a_{k + 1})$ be a sequence of…2025 · 2 Apr · Shift 2 · Q35 · MCQ
Let $A = {- 3, - 2, - 1, 0, 1, 2, 3}$ . Let R be a relation on A defined by $x R y$ if and only if $0 \leq x^{2} + 2 y \leq 4$ . Let $l$ be the number of elements in R and $m$ be the minimum number of elements required to be added in R…2025 · 3 Apr · Shift 1 · Q30 · MCQ
Let $A = {- 2, - 1, 0, 1, 2, 3}$ . Let R be a relation on $A$ defined by $x R y$ if and only if $y = max {x, 1}$ . Let $l$ be the number of elements in R . Let $m$ and $n$ be the minimum number of elements required to be added in R to…2025 · 3 Apr · Shift 2 · Q36 · MCQ
Consider the sets $A = {(x, y) \in R \times R : x^{2} + y^{2} = 25}, B = {(x, y) \in R \times R : x^{2} + 9 y^{2} = 144}$ , $C = {(x, y) \in Z \times Z : x^{2} + y^{2} \leq 4}$ …2025 · 4 Apr · Shift 1 · Q31 · MCQ
Let $A = {- 3, - 2, - 1, 0, 1, 2, 3}$ and R be a relation on A defined by $x R y$ if and only if $2 x - y \in {0, 1}$ . Let $l$ be the number of elements in $R$ . Let $m$ and $n$ be the minimum number of elements required to be added…2025 · 4 Apr · Shift 2 · Q26 · MCQ
The number of relations on the set $A = {1, 2, 3}$ , containing at most 6 elements including $(1, 2)$ , which are reflexive and transitive but not symmetric, is .2025 · 7 Apr · Shift 1 · Q47 · Numerical
For $n \geq 2$ , let $S_{n}$ denote the set of all subsets of ${1, 2, \dots, n}$ with no two consecutive numbers. For example ${1, 3, 5} \in S_{6}$ , but ${1, 2, 4} \in / S_{6}$ . Then $n (S_{5})$ is equal to 2025 · 7 Apr · Shift 1 · Q49 · Numerical
Let A = { ( $α, β$ ) $\in R \times R$ : | $α$ - 1| $\leq 4$ and | $β$ - 5| $\leq 6$ } and B = { ( $α, β$ ) $\in R \times R$ : 16( $α$ - $2)^{2}$ + 9( $β$ - $6)^{2} \leq 144$ }. Then2025 · 7 Apr · Shift 2 · Q40 · MCQ
Let A = {0, 1, 2, 3, 4, 5}. Let R be a relation on A defined by (x, y) ∈ R if and only if max{x, y} ∈ {3, 4}. Then among the statements (S1): The number of elements in R is 18, and (S2): The relation R is symmetric but neither reflexive…2025 · 8 Apr · Shift 2 · Q39 · MCQ
Let $A = {1, 2, 3, \dots, 10}$ and $B = {\frac{m}{n} : m, n \in A, m < n$ and $gcd (m, n) = 1}$ . Then $n (B)$ is equal to :2025 · 22 Jan · Shift 1 · Q29 · MCQ
The number of non-empty equivalence relations on the set ${1, 2, 3}$ is :2025 · 22 Jan · Shift 1 · Q40 · MCQ
Let $A = {1, 2, 3}$ . The number of relations on $A$ , containing $(1, 2)$ and $(2, 3)$ , which are reflexive and transitive but not symmetric, is .2025 · 22 Jan · Shift 2 · Q50 · Numerical
Let $R = {(1, 2), (2, 3), (3, 3)}$ be a relation defined on the set ${1, 2, 3, 4}$ . Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:2025 · 23 Jan · Shift 1 · Q45 · MCQ
Let $X = R \times R$ . Define a relation R on X as : $(a_{1}, b_{1}) R (a_{2}, b_{2}) \Leftrightarrow b_{1} = b_{2}$ Statement I: $R$ is an equivalence relation. Statement II : For some $(a, b) \in X$ …2025 · 23 Jan · Shift 2 · Q32 · MCQ
Let $A = {(x, y) \in R \times R : ∣ x + y ∣ ⩾ 3}$ and $B = {(x, y) \in R \times R : ∣ x ∣ + ∣ y ∣ \leq 3}$ . If $C = {(x, y) \in A \cap B : x = 0$ or $y = 0}$ , then $\sum_{(x, y) \in C} ∣ x + y ∣$ …2025 · 23 Jan · Shift 2 · Q39 · MCQ
Let $S = {p_{1}, p_{2} \dots, p_{10}}$ be the set of first ten prime numbers. Let $A = S \cup P$ , where $P$ is the set of all possible products of distinct elements of $S$ . Then the number of all ordered pairs $(x, y), x \in S$ , $y \in A$ …2025 · 24 Jan · Shift 1 · Q48 · Numerical
Let $A = {x \in (0, π) - {\frac{π}{2}} : lo g_{(2/ π)} ∣ sin x ∣ + lo g_{(2/ π)} ∣ cos x ∣ = 2}$ and $B = {x ⩾ 0 : x (x - 4) - 3∣ x - 2∣ + 6 = 0}$ . Then $n (A \cup B)$ …2025 · 24 Jan · Shift 2 · Q29 · MCQ
The relation $R = {(x, y) : x, y \in Z$ and $x + y$ is even $}$ is:2025 · 28 Jan · Shift 1 · Q29 · MCQ
Define a relation R on the interval $[0, \frac{π}{2})$ by $x$ R $y$ if and only if $sec^{2} x - tan^{2} y = 1$ . Then R is :2025 · 29 Jan · Shift 1 · Q43 · MCQ
Let $S = N \cup {0}$ . Define a relation R from S to $R$ by : $R = {(x, y) : lo g_{e} y = x lo g_{e} (\frac{2}{5}), x \in S, y \in R} .$ Then, the…2025 · 29 Jan · Shift 2 · Q26 · MCQ
Let $A = {1, 2, 3, \dots, 20}$ . Let $R_{1}$ and $R_{2}$ two relation on $A$ such that $R_{1} = {(a, b) : b$ is divisible by $a} R_{2} = {(a, b) : a$ is an integral multiple of $b}$ . Then, number of elements in $R_{1} - R_{2}$ is equal to …2024 · 1 Feb · Shift 1 · Q60 · Numerical
Consider the relations $R_{1}$ and $R_{2}$ defined as $a R_{1} b \Leftrightarrow a^{2} + b^{2} = 1$ for all $a, b \in R$ and $(a, b) R_{2} (c, d) \Leftrightarrow a + d = b + c$ for all $(a, b), (c, d) \in N \times N$ . Then :2024 · 1 Feb · Shift 2 · Q34 · MCQ
In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied…2024 · 4 Apr · Shift 1 · Q57 · Numerical
Let a relation $R$ on $N \times N$ be defined as: $(x_{1}, y_{1}) R (x_{2}, y_{2})$ if and only if $x_{1} \leq x_{2}$ or $y_{1} \leq y_{2}$ . Consider the two statements: (I) $R$ is…2024 · 4 Apr · Shift 2 · Q48 · MCQ
Let $A = {n \in [100, 700] \cap N : n$ is neither a multiple of 3 nor a multiple of 4 $}$ . Then the number of elements in $A$ is2024 · 6 Apr · Shift 1 · Q33 · MCQ
Let the relations $R_{1}$ and $R_{2}$ on the set $X = {1, 2, 3, \dots, 20}$ be given by $R_{1} = {(x, y) : 2 x - 3 y = 2}$ and $R_{2} = {(x, y) : - 5 x + 4 y = 0}$ . If $M$ and $N$ be the minimum number of elements required to be added in $R_{1}$ and $R_{2}$ ,…2024 · 6 Apr · Shift 1 · Q36 · MCQ
Let $A = {1, 2, 3, 4, 5}$ . Let $R$ be a relation on $A$ defined by $x R y$ if and only if $4 x \leq 5 y$ . Let $m$ be the number of elements in $R$ and $n$ be the minimum…2024 · 6 Apr · Shift 2 · Q32 · MCQ
Let $A = {2, 3, 6, 8, 9, 11}$ and $B = {1, 4, 5, 10, 15}$ . Let $R$ be a relation on $A \times B$ defined by $(a, b) R (c, d)$ if and only if $3 a d - 7 b c$ is an even integer. Then the relation $R$ is2024 · 8 Apr · Shift 2 · Q43 · MCQ
Let $A = {2, 3, 6, 7}$ and $B = {4, 5, 6, 8}$ . Let $R$ be a relation defined on $A \times B$ by $(a_{1}, b_{1}) R (a_{2}, b_{2})$ if and only if $a_{1} + a_{2} = b_{1} + b_{2}$ . Then the number of elements in $R$ is .2024 · 9 Apr · Shift 1 · Q51 · Numerical
Let $S = {1, 2, 3, \dots, 10}$ . Suppose $M$ is the set of all the subsets of $S$ , then the relation $R = {(A, B) : A \cap B e q ϕ; A, B \in M}$ is :2024 · 27 Jan · Shift 1 · Q33 · MCQ
Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of the set $A$ is 56 more than the total number of subsets of $B$ . Then the distance of the point $P (m, n)$ from the point $Q (- 2, - 3)$ is…2024 · 27 Jan · Shift 2 · Q36 · MCQ
Let $R$ be a relation on $Z \times Z$ defined by $(a, b) R (c, d)$ if and only if $a d - b c$ is divisible by 5. Then $R$ is2024 · 29 Jan · Shift 1 · Q39 · MCQ
If R is the smallest equivalence relation on the set ${1, 2, 3, 4}$ such that ${(1, 2), (1, 3)} \subset R$ , then the number of elements in $R$ is .2024 · 29 Jan · Shift 2 · Q37 · MCQ
The number of symmetric relations defined on the set ${1, 2, 3, 4}$ which are not reflexive is .2024 · 30 Jan · Shift 2 · Q58 · Numerical
Let $A = {1, 2, 3, 4}$ and $R = {(1, 2), (2, 3), (1, 4)}$ be a relation on $A$ . Let $S$ be the equivalence relation on $A$ such that $R \subset S$ and the number of elements in $S$ is $n$ . Then, the…2024 · 31 Jan · Shift 1 · Q59 · Numerical
Let $A = {1, 2, 3, \dots\dots\dots\dots, 100}$ . Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $2 x = 3 y$ . Let $R_{1}$ be a symmetric relation on $A$ such that $R \subset R_{1}$ and the number of elements in…2024 · 31 Jan · Shift 2 · Q57 · Numerical
Let $R$ be a relation on $R$ , given by $R = {(a, b) : 3 a - 3 b + 7$ is an irrational number $}$ . Then $R$ is2023 · 1 Feb · Shift 1 · Q24 · MCQ
Let $P (S)$ denote the power set of $S = {1, 2, 3, \dots ., 10}$ . Define the relations $R_{1}$ and $R_{2}$ on $P (S)$ as $AR_{1} B$ if $(A \cap B^{c}) \cup (B \cap A^{c}) = \emptyset$ …2023 · 1 Feb · Shift 2 · Q25 · MCQ
Let $A = {1, 2, 3, 4, \dots ., 10}$ and $B = {0, 1, 2, 3, 4}$ . The number of elements in the relation $R = {(a, b) \in A \times A : 2 (a - b)^{2} + 3 (a - b) \in B}$ is .2023 · 6 Apr · Shift 1 · Q40 · Numerical
Let $A = {0, 3, 4, 6, 7, 8, 9, 10}$ and $R$ be the relation defined on $A$ such that $R = {(x, y) \in A \times A : x - y$ is odd positive integer or $x - y = 2}$ . The minimum number of elements that must be added to the relation $R$ , so that it is a…2023 · 8 Apr · Shift 1 · Q40 · Numerical
Let $A = {1, 2, 3, 4, 5, 6, 7}$ . Then the relation $R = {(x, y) \in A \times A : x + y = 7}$ is :2023 · 8 Apr · Shift 2 · Q26 · MCQ
The number of elements in the set ${n \in Z : ∣ n^{2} - 10 n + 19∣ < 6}$ is .2023 · 10 Apr · Shift 1 · Q41 · Numerical
Let $A = {2, 3, 4}$ and $B = {8, 9, 12}$ . Then the number of elements in the relation $R = {((a_{1}, b_{1}), (a_{2}, b_{2})) \in (A \times B, A \times B) : a_{1}$ …2023 · 10 Apr · Shift 2 · Q32 · MCQ
An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?2023 · 11 Apr · Shift 1 · Q40 · MCQ
Let $A = {1, 3, 4, 6, 9}$ and $B = {2, 4, 5, 8, 10}$ . Let $R$ be a relation defined on $A \times B$ such that $R = {((a_{1}, b_{1}), (a_{2}, b_{2})) : a_{1} \leq b_{2}$ …2023 · 11 Apr · Shift 2 · Q28 · MCQ
The number of relations, on the set ${1, 2, 3}$ containing $(1, 2)$ and $(2, 3)$ , which are reflexive and transitive but not symmetric, is .2023 · 12 Apr · Shift 1 · Q40 · Numerical
Let $A = {- 4, - 3, - 2, 0, 1, 3, 4}$ and $R = {(a, b) \in A \times A : b = ∣ a ∣$ or $b^{2} = a + 1}$ be a relation on $A$ . Then the minimum number of elements, that must be added to…2023 · 13 Apr · Shift 2 · Q36 · Numerical
The number of elements in the set ${n \in N : 10 \leq n \leq 100$ and $3^{n} - 3$ is a multiple of 7 $}$ is .2023 · 15 Apr · Shift 1 · Q43 · Numerical
Let $A = {1, 2, 3, 4}$ and $R$ be a relation on the set $A \times A$ defined by $R = {((a, b), (c, d)) : 2 a + 3 b = 4 c + 5 d}$ . Then the number of elements in $R$ is .2023 · 15 Apr · Shift 1 · Q44 · Numerical
The relation $R = {(a, b) : g cd (a, b) = 1, 2aeb, a, b \in Z}$ is :2023 · 24 Jan · Shift 1 · Q26 · MCQ
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 .2023 · 24 Jan · Shift 2 · Q37 · Numerical
Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is .2023 · 25 Jan · Shift 1 · Q40 · Numerical
Let R be a relation defined on $N$ as $a R b$ if $2 a + 3 b$ is a multiple of $5, a, b \in N$ . Then R is2023 · 29 Jan · Shift 2 · Q25 · MCQ
The minimum number of elements that must be added to the relation $R = {(a, b), (b, c)}$ on the set ${a, b, c}$ so that it becomes symmetric and transitive is :2023 · 30 Jan · Shift 1 · Q24 · MCQ
Let $R$ be a relation on $N \times N$ defined by $(a, b) R (c, d)$ if and only if $a d (b - c) = b c (a - d)$ . Then $R$ is2023 · 31 Jan · Shift 1 · Q30 · MCQ
Among the relations $S = {(a, b) : a, b \in R - {0}, 2 + \frac{a}{b} > 0}$ and $T = {(a, b) : a, b \in R, a^{2} - b^{2} \in Z}$ …2023 · 31 Jan · Shift 2 · Q31 · MCQ
The sum of all the elements of the set ${α \in {1, 2, ....., 100} : H C F (α, 24) = 1}$ is .2022 · 24 Jun · Shift 2 · Q40 · Numerical
Let $A = {1, 2, 3, 4, 5, 6, 7}$ . Define $B = {T \subseteq A$ : either $1 o t in T$ or $2 \in T}$ and $C = {T \subseteq A : T$ the sum of all the elements of $T$ is a prime number $}$ . Then the number of elements in the set $B \cup C$ is …2022 · 25 Jul · Shift 2 · Q37 · Numerical
Let $A = {1, 2, 3, 4, 5, 6, 7}$ and $B = {3, 6, 7, 9}$ . Then the number of elements in the set ${C \subseteq A : C \cap B e q ϕ}$ is .2022 · 26 Jul · Shift 2 · Q34 · Numerical
Let A = {n $\in$ N : H.C.F. (n, 45) = 1} and Let B = {2k : k $\in$ {1, 2, ......., 100}}. Then the sum of all the elements of A $\cap$ B is .2022 · 26 Jun · Shift 1 · Q38 · Numerical
Let $A = i = 1 \sum 10 j = 1 \sum 10 min {i, j}$ and $B = i = 1 \sum 10 j = 1 \sum 10 max {i, j}$ . Then A + B is equal to .2022 · 26 Jun · Shift 1 · Q40 · Numerical
Let $R_{1}$ and $R_{2}$ be two relations defined on $R$ by $a R_{1} b \Leftrightarrow ab \geq 0$ and $a R_{2} b \Leftrightarrow a \geq b$ Then,2022 · 27 Jul · Shift 1 · Q24 · MCQ
For $α \in N$ , consider a relation $R$ on $N$ given by $R = {(x, y) : 3 x + α y$ is a multiple of 7 $}$ . The relation $R$ is an equivalence relation if and only if :2022 · 28 Jul · Shift 1 · Q29 · MCQ
Let R1 and R2 be relations on the set {1, 2, ......., 50} such that R1 = {(p, pn) : p is a prime and n $\geq$ 0 is an integer} and R2 = {(p, pn) : p is a prime and n = 0 or 1}. Then, the number of elements in R1 $-$ R2 is …2022 · 28 Jun · Shift 1 · Q35 · Numerical
Let R1 = {(a, b) $\in$ N $\times$ N : |a $-$ b| $\leq$ 13} and R2 = {(a, b) $\in$ N $\times$ N : |a $-$ b| $e$ 13}. Then on N :2022 · 28 Jun · Shift 2 · Q22 · MCQ
Let R be a relation from the set ${1, 2, 3, \dots, 60}$ to itself such that $R = {(a, b) : b = pq$ , where $p, q ⩾ 3$ are prime numbers}. Then, the number of elements in R is :2022 · 29 Jul · Shift 1 · Q25 · MCQ
Let $S = {4, 6, 9}$ and $T = {9, 10, 11, \dots, 1000}$ . If $A = {a_{1} + a_{2} + \dots + a_{k} : k \in N, a_{1}, a_{2}, a_{3}, \dots, a_{k}$ $ϵ S}$ , then the sum of all the elements in the set $T - A$ is equal to …2022 · 29 Jul · Shift 1 · Q46 · Numerical
Let a set A = A1 $\cup$ A2 $\cup$ ..... $\cup$ Ak, where Ai $\cap$ Aj = $ϕ$ for i $e$ j, 1 $\leq$ j, j $\leq$ k. Define the relation R from A to A by R = {(x, y) : y $\in$ Ai if and only if x $\in$ Ai, 1 $\leq$ i $\leq$ k}. Then, R is :2022 · 29 Jun · Shift 1 · Q28 · MCQ
The number of elements in the set {x $\in$ R : (|x| $-$ 3) |x + 4| = 6} is equal to :2021 · 16 Mar · Shift 1 · Q26 · MCQ
Let A = {2, 3, 4, 5, ....., 30} and ' $≃$ ' be an equivalence relation on A $\times$ A, defined by (a, b) $≃$ (c, d), if and only if ad = bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered…2021 · 16 Mar · Shift 2 · Q33 · MCQ
In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement? Includes diagram2021 · 17 Mar · Shift 1 · Q33 · MCQ
Define a relation R over a class of n $\times$ n real matrices A and B as "ARB iff there exists a non-singular matrix P such that PAP $-$ 1 = B". Then which of the following is true?2021 · 18 Mar · Shift 2 · Q33 · MCQ
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 …2021 · 24 Feb · Shift 1 · Q40 · Numerical
Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :2021 · 26 Aug · Shift 1 · Q28 · MCQ
Let R = {(P, Q) | P and Q are at the same distance from the origin} be a relation, then the equivalence class of (1, $-$ 1) is the set :2021 · 26 Feb · Shift 1 · Q28 · MCQ
If A = {x $\in$ R : |x $-$ 2| > 1}, B = {x $\in$ R : $x^{2} - 3$ > 1}, C = {x $\in$ R : |x $-$ 4| $\geq$ 2} and Z is the set of all integers, then the number of subsets of the set (A $\cap$ B $\cap$ C)c $\cap$ Z is …2021 · 27 Aug · Shift 1 · Q36 · Numerical
Let N be the set of natural numbers and a relation R on N be defined by $R = {(x, y) \in N \times N : x^{3} - 3 x^{2} y - x y^{2} + 3 y^{3} = 0}$ . Then the relation R is :2021 · 27 Jul · Shift 2 · Q35 · MCQ
Let A = {n $\in$ N | n2 $\leq$ n + 10,000}, B = {3k + 1 | k $\in$ N} an dC = {2k | k $\in$ N}, then the sum of all the elements of the set A $\cap$ (B $-$ C) is equal to .2021 · 27 Jul · Shift 2 · Q43 · Numerical
Which of the following is not correct for relation R on the set of real numbers ?2021 · 31 Aug · Shift 1 · Q27 · MCQ
If R = {(x, y) : x, y $\in$ Z, x2 + 3y2 $\leq$ 8} is a relation on the set of integers Z, then the domain of R–1 is :2020 · 2 Sep · Shift 1 · Q35 · MCQ
Consider the two sets : A = {m $\in$ R : both the roots of x2 – (m + 1)x + m + 4 = 0 are real} and B = [–3, 5). Which of the following is not true?2020 · 3 Sep · Shift 1 · Q30 · MCQ
Let R1 and R2 be two relation defined as follows : R1 = {(a, b) $\in$ R2 : a2 + b2 $\in$ Q} and R2 = {(a, b) $\in$ R2 : a2 + b2 $o t in$ Q}, where Q is the set of all rational numbers. Then :2020 · 3 Sep · Shift 2 · Q25 · MCQ
A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If x% of the people read both the newspapers, then a possible value of x can be:2020 · 4 Sep · Shift 1 · Q22 · MCQ
Let $i = 1 \cup 50 X_{i} = i = 1 \cup n Y_{i} = T$ where each Xi contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xi’s and…2020 · 4 Sep · Shift 2 · Q37 · MCQ
A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be :2020 · 5 Sep · Shift 1 · Q31 · MCQ
Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m.n is .2020 · 6 Sep · Shift 1 · Q25 · Numerical
Let X = {n $\in$ N : 1 $\leq$ n $\leq$ 50}. If A = {n $\in$ X: n is a multiple of 2} and B = {n $\in$ X: n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is .2020 · 7 Jan · Shift 2 · Q31 · Numerical
If A = {x $\in$ R : |x| < 2} and B = {x $\in$ R : |x – 2| $\geq$ 3}; then :2020 · 9 Jan · Shift 2 · Q30 · MCQ
Two newspapers A and B are published in a city. It is known that 25% of the city populations reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into advertisements and 40% of those who read…2019 · 9 Apr · Shift 2 · Q33 · MCQ
In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number…2019 · 10 Jan · Shift 1 · Q28 · MCQ
Let A, B and C be sets such that $ϕ e$ A $\cap$ B $\subseteq$ C. Then which of the following statements is not true ?2019 · 12 Apr · Shift 2 · Q23 · MCQ
Let S = {1, 2, 3, … , 100}. The number of non-empty subsets A of S such that the product of elements in A is even is :2019 · 12 Jan · Shift 1 · Q27 · MCQ
Let Z be the set of integers. If A = {x $\in$ Z : 2(x + 2) (x2 $-$ 5x + 6) = 1} and B = {x $\in$ Z : $-$ 3 < 2x $-$ 1 < 9}, then the number of subsets of the set A $\times$ B, is2019 · 12 Jan · Shift 2 · Q40 · MCQ
Consider the following two binary relations on the set A = {a, b, c} : R1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)} and R2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}. Then :2018 · 15 Apr · Shift 1 · Q32 · MCQ
Let N denote the set of all natural numbers. Define two binary relations on N as R = {(x, y) $\in$ N $\times$ N : 2x + y = 10} and R2 = {(x, y) $\in$ N $\times$ N : x + 2y = 10}. Then :2018 · 16 Apr · Shift 1 · Q36 · MCQ
Two sets A and B are as under : A = {( $a$ , b) $\in$ R $\times$ R : | $a$ - 5| < 1 and |b - 5| < 1}; B = {( $a$ , b) $\in$ R $\times$ R : 4( $a$ - 6)2 + 9(b - 5)2 $\leq$ 36 }; Then2018 · Shift 0 · Q32 · MCQ
Let P = { $θ$ : sin $θ -$ cos $θ$ = $2 cos θ$ } and Q = { $θ$ : sin $θ$ + cos $θ$ = $2 sin θ$ } be two sets. Then2016 · 10 Apr · Shift 1 · Q27 · MCQ
Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A $\times$ B , each having atleast three elements are2015 · Shift 0 · Q42 · MCQ
Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y $\subseteq$ X, Z $\subseteq$ X and Y $\cap$ Z is empty, is :2012 · Shift 0 · Q23 · MCQ
Let $R$ be the set of real numbers. Statement I : $A = {(x, y) \in R \times R : y - x$ is an integer $}$ is an equivalence relation on $R$ . Statement II : $B = {(x, y) \in R \times R : x = α y$ for some rational number $α}$ is an…2011 · Shift 0 · Q51 · MCQ
Consider the following relations $R = {(x, y) ∣ x, y$ are real numbers and $x = w y$ for some rational number $w}$ ; $S = {(\frac{m}{n}, \frac{p}{q}) ∣ m, n, p$ and $q$ are integers such that $n, q e q 0$ and $q m = p m}$ …2010 · Shift 0 · Q50 · MCQ
If $A, B$ and $C$ are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ , then :2009 · Shift 0 · Q47 · MCQ
Let R be the real line. Consider the following subsets of the plane $R \times R$ : $S = {(x, y) : y = x + 1 an d 0 < x < 2} T = {(x, y) : x - y i s an int e g er}$ , Which one…2008 · Shift 0 · Q53 · MCQ
Let $W$ denote the words in the English dictionary. Define the relation $R$ by $R = {(x, y) \in W \times W ∣$ the words $x$ and $y$ have at least one letter in common}. Then, $R$ is2006 · Shift 0 · Q82 · MCQ
Let $R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12)$ , $(3, 9), (3, 12), (3, 6)}$ be a relation on the set $A = {3, 6, 9, 12}$ . The relation is :2005 · Shift 0 · Q114 · MCQ
Let $R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)}$ be a relation on the set $A = {1, 2, 3, 4}$ . The relation $R$ is :2004 · Shift 0 · Q116 · MCQ