1
JEE Main 2024 (Online) 30th January Evening Shift
Numerical
+4
-1

The number of symmetric relations defined on the set $$\{1,2,3,4\}$$ which are not reflexive is _________.

2
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
The number of elements in the set

$\left\{n \in \mathbb{N}: 10 \leq n \leq 100\right.$ and $3^{n}-3$ is a multiple of 7$\}$ is ___________.
3
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
Let $A=\{1,2,3,4\}$ and $\mathrm{R}$ be a relation on the set $A \times A$ defined by

$R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}$. Then the number of elements in $\mathrm{R}$ is ____________.
4
JEE Main 2023 (Online) 13th April Evening Shift
Numerical
+4
-1

Let $$\mathrm{A}=\{-4,-3,-2,0,1,3,4\}$$ and $$\mathrm{R}=\left\{(a, b) \in \mathrm{A} \times \mathrm{A}: b=|a|\right.$$ or $$\left.b^{2}=a+1\right\}$$ be a relation on $$\mathrm{A}$$. Then the minimum number of elements, that must be added to the relation $$\mathrm{R}$$ so that it becomes reflexive and symmetric, is __________