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

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 __________.

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2
JEE Main 2024 (Online) 30th January Evening Shift
Numerical
+4
-1
Change Language

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

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3
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
Change Language
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 ___________.
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4
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
Change Language
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 ____________.
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