1
JEE Main 2024 (Online) 31st January Evening Shift
Numerical
+4
-1

Let $$A=\{1,2,3, \ldots \ldots \ldots \ldots, 100\}$$. Let $$R$$ be a relation on $$\mathrm{A}$$ defined by $$(x, y) \in R$$ if and only if $$2 x=3 y$$. Let $$R_1$$ be a symmetric relation on $$A$$ such that $$R \subset R_1$$ and the number of elements in $$R_1$$ is $$\mathrm{n}$$. Then, the minimum value of $$\mathrm{n}$$ is _________.

2
JEE Main 2024 (Online) 31st January Morning Shift
Numerical
+4
-1

Let $$A=\{1,2,3,4\}$$ and $$R=\{(1,2),(2,3),(1,4)\}$$ be a relation on $$\mathrm{A}$$. Let $$\mathrm{S}$$ be the equivalence relation on $$\mathrm{A}$$ such that $$R \subset S$$ and the number of elements in $$\mathrm{S}$$ is $$\mathrm{n}$$. Then, the minimum value of $$n$$ is __________.

3
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 _________.

4
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 ___________.