1
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

If R is the smallest equivalence relation on the set $$\{1,2,3,4\}$$ such that $$\{(1,2),(1,3)\} \subset \mathrm{R}$$, then the number of elements in $$\mathrm{R}$$ is __________.

A
15
B
10
C
12
D
8
2
JEE Main 2024 (Online) 29th January Morning Shift
+4
-1

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 $$R$$ is

A
Reflexive and transitive but not symmetric
B
Reflexive and symmetric but not transitive
C
Reflexive but neither symmetric nor transitive
D
Reflexive, symmetric and transitive
3
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

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 :

A
8
B
10
C
4
D
6
4
JEE Main 2024 (Online) 27th January Morning Shift
+4
-1
Let $S=\{1,2,3, \ldots, 10\}$. Suppose $M$ is the set of all the subsets of $S$, then the relation

$\mathrm{R}=\{(\mathrm{A}, \mathrm{B}): \mathrm{A} \cap \mathrm{B} \neq \phi ; \mathrm{A}, \mathrm{B} \in \mathrm{M}\}$ is :
A
symmetric only
B
reflexive only
C
symmetric and reflexive only
D
symmetric and transitive only
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