1
JEE Main 2023 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+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
2
JEE Main 2023 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+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
3
JEE Main 2023 (Online) 24th January Morning Shift
MCQ (Single Correct Answer)
+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
4
JEE Main 2022 (Online) 29th July Morning Shift
MCQ (Single Correct Answer)
+4
-1

Let R be a relation from the set $$\{1,2,3, \ldots, 60\}$$ to itself such that $$R=\{(a, b): b=p q$$, where $$p, q \geqslant 3$$ are prime numbers}. Then, the number of elements in R is :

A
600
B
660
C
540
D
720
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