1
JEE Main 2024 (Online) 1st February Evening Shift
+4
-1
Consider the relations $R_1$ and $R_2$ defined as $a R_1 b \Leftrightarrow a^2+b^2=1$ for all $a, b \in \mathbf{R}$ and $(a, b) R_2(c, d) \Leftrightarrow$ $a+d=b+c$ for all $(a, b),(c, d) \in \mathbf{N} \times \mathbf{N}$. Then :
A
$R_1$ and $R_2$ both are equivalence relations
B
Only $R_1$ is an equivalence relation
C
Only $R_2$ is an equivalence relation
D
Neither $R_1$ nor $R_2$ is an equivalence relation
2
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
3
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
4
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
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