Types of Relations

JEE Main Mathematics · Relations and Functions · 32 questions, latest first

• Let R={(x, y) ∈ N × N: log_e(x+y) ≤ 2}. Then the minimum number of elements, required to be added in R to make it a transitive…20266 April, Shift 2 · Q21
• Let A={-2,-1,0,1,2,3,4}. Let R be a relation on A defined by x R y if and only if 2 x+y ≤ 2. Let l be the number of elements in…202623 January, Shift 1 · Q1
• Let the relation R on the set M={1,2,3, …, 16} be given by R={(x, y): 4 y=5 x-3, x, y ∈ M}. Then the minimum number of elements…202622 January, Shift 1 · Q1
• Let A={2,3,5,7,9}. Let R be the relation on A defined by x R y if and only if 2 x ≤ 3 y. Let l be the number of elements in R,…202621 January, Shift 2 · Q1
• The number of relations, defined on the set \{a, b, c, d\}, which are both reflexive and symmetric, is equal to:202621 January, Shift 1 · Q1
• 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…20258 April, Shift 2 · Q1
• The number of relations on the set A={1,2,3}, containing at most 6 elements including ( 1,2 ), which are reflexive and transitive…20257 April, Shift 1 · Q24
• 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 ∈{0,1}. Let l be the number of elements…20254 April, Shift 2 · Q2
• 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…20253 April, Shift 2 · Q1
• 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 ≤ x^2+2 y ≤ 4. Let l be the number of…20253 April, Shift 1 · Q1
• Let A be the set of all functions f: Z → 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:20252 April, Shift 1 · Q12
• Define a relation R on the interval [0, (π)/2) by x R y if and only if sec^2 x- tan^2 y=1. Then R is:202529 January, Shift 1 · Q1
• The relation R={(x, y): x, y ∈ Z and x+y is even } is:202528 January, Shift 1 · Q1
• 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…202522 January, Shift 2 · Q25
• Let A={2,3,6,8,9,11} and B={1,4,5,10,15}. Let R be a relation on A × B defined by (a, b) R(c, d) if and only if 3 ad-7 bc is an…20248 April, Shift 2 · Q1
• 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 ≤ 5 y. Let m be the number of elements in R and n…20246 April, Shift 2 · Q2
• Let the relations R_1 and R_2 on the set X={1,2,3, …., 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…20246 April, Shift 1 · Q1
• Let a relation R on N × N be defined as: (x_1, y_1) R(x_2, y_2) if and only if x_1 ≤ x_2 or y_1 ≤ y_2. Consider the two…20244 April, Shift 2 · Q1
• Let A={1,2,3, …, 100}. Let R be a relation on A defined by (x, y) ∈ R if and only if 2 x=3 y. Let R_1 be a symmetric relation on…202431 January, Shift 2 · Q21
• The number of symmetric relations defined on the set {1,2,3,4} which are not reflexive is ____.202430 January, Shift 2 · Q21
• Let R be a relation on Z × Z defined by (a, b) R(c, d) if and only if ad-bc is divisible by 5. Then R is202429 January, Shift 1 · Q2
• Let S={1,2,3, …, 10}. Suppose M is the set of all the subsets of S, then the relation R={(A, B): A ∩ B ≠ φ; A, B ∈ M} is:202427 January, Shift 1 · Q1
• Let A={-4,-3,-2,0,1,3,4} and R={(a, b) ∈ A × A: b=|a|. or.b^2=a+1} be a relation on A. Then the minimum number of elements, that…202313 April, Shift 2 · Q21
• The number of relations, on the set {1,2,3} containing ( 1,2 ) and ( 2,3 ), which are reflexive and transitive but not symmetric,…202312 April, Shift 1 · Q21
• Let A={1,2,3,4,5,6,7}. Then the relation R={(x, y) ∈ A × A: x+y=7} is20238 April, Shift 2 · Q1
• Let A={0,3,4,6,7,8,9,10} and R be the relation defined on A such that R={(x, y) ∈ A × A: x-y is odd positive integer or x-y=2}.…20238 April, Shift 1 · Q21
• Let R be a relation on R, given by R={(a, b): 3 a-3 b+√7 is an irrational number }. Then R is20231 February, Shift 1 · Q61
• Among the relations S={(a, b): a, b ∈ R-{0}, 2+a/b>0} and T={(a, b): a, b ∈ R, a^2-b^2 ∈ Z},202331 January, Shift 2 · Q61
• Let R be a relation on N × N defined by (a, b) R(c, d) if and only if a d(b-c)=b c(a-d). Then R is202331 January, Shift 1 · Q61
• 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…202330 January, Shift 1 · Q61
• Let R be a relation defined on N as a R b if 2 a+3 b is a multiple of 5, a, b ∈ N. Then R is202329 January, Shift 2 · Q61
• The relation R={(a, b): gcd(a, b)=1,2 a ≠ b, a, b ∈ Z} is:202324 January, Shift 1 · Q62