1
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
2
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
3
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
4
JEE Main 2023 (Online) 11th April Evening Shift
+4
-1

Let $$\mathrm{A}=\{1,3,4,6,9\}$$ and $$\mathrm{B}=\{2,4,5,8,10\}$$. Let $$\mathrm{R}$$ be a relation defined on $$\mathrm{A} \times \mathrm{B}$$ such that $$\mathrm{R}=\left\{\left(\left(a_{1}, b_{1}\right),\left(a_{2}, b_{2}\right)\right): a_{1} \leq b_{2}\right.$$ and $$\left.b_{1} \leq a_{2}\right\}$$. Then the number of elements in the set R is :

A
180
B
26
C
52
D
160
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