1
JEE Main 2023 (Online) 31st January Morning Shift
+4
-1

Let $$\mathrm{R}$$ be a relation on $$\mathrm{N} \times \mathbb{N}$$ defined by $$(a, b) ~\mathrm{R}~(c, d)$$ if and only if $$a d(b-c)=b c(a-d)$$. Then $$\mathrm{R}$$ is

A
symmetric and transitive but not reflexive
B
reflexive and symmetric but not transitive
C
transitive but neither reflexive nor symmetric
D
symmetric but neither reflexive nor transitive
2
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1

The minimum number of elements that must be added to the relation $$\mathrm{R}=\{(\mathrm{a}, \mathrm{b}),(\mathrm{b}, \mathrm{c})\}$$ on the set $$\{a, b, c\}$$ so that it becomes symmetric and transitive is :

A
7
B
3
C
4
D
5
3
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1

Let R be a relation defined on $$\mathbb{N}$$ as $$a\mathrm{R}b$$ if $$2a+3b$$ is a multiple of $$5,a,b\in \mathbb{N}$$. Then R is

A
an equivalence relation
B
non reflexive
C
symmetric but not transitive
D
transitive but not symmetric
4
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1

The relation $$\mathrm{R = \{ (a,b):\gcd (a,b) = 1,2a \ne b,a,b \in \mathbb{Z}\}}$$ is :

A
reflexive but not symmetric
B
transitive but not reflexive
C
symmetric but not transitive
D
neither symmetric nor transitive
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination