1
JEE Main 2024 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language
Let $A=\{1,2,3, \ldots, 20\}$. Let $R_1$ and $R_2$ two relation on $A$ such that

$R_1=\{(a, b): b$ is divisible by $a\}$

$R_2=\{(a, b): a$ is an integral multiple of $b\}$.

Then, number of elements in $R_1-R_2$ is equal to _____________.
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2
JEE Main 2024 (Online) 31st January Evening Shift
Numerical
+4
-1
Change Language

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 _________.

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3
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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4
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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