1
JEE Main 2025 (Online) 22nd January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of non-empty equivalence relations on the set $\{1,2,3\}$ is :

A
7
B
4
C
5
D
6
2
JEE Main 2024 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 $$R$$ is

A
reflexive but not symmetric.
B
an equivalence relation.
C
reflexive and symmetric but not transitive.
D
transitive but not symmetric.
3
JEE Main 2024 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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

A
23
B
26
C
25
D
24
4
JEE Main 2024 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$A=\{n \in[100,700] \cap \mathrm{N}: n$$ is neither a multiple of 3 nor a multiple of 4$$\}$$. Then the number of elements in $$A$$ is

A
300
B
310
C
290
D
280
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