1
JEE Main 2023 (Online) 12th April Morning Shift
Numerical
+4
-1

The number of relations, on the set $$\{1,2,3\}$$ containing $$(1,2)$$ and $$(2,3)$$, which are reflexive and transitive but not symmetric, is __________.

2
JEE Main 2023 (Online) 10th April Morning Shift
Numerical
+4
-1

The number of elements in the set $$\{ n \in Z:|{n^2} - 10n + 19| < 6\}$$ is _________.

3
JEE Main 2023 (Online) 8th April Morning Shift
Numerical
+4
-1

Let $$A=\{0,3,4,6,7,8,9,10\}$$ and $$R$$ be the relation defined on $$A$$ such that $$R=\{(x, y) \in A \times A: x-y$$ is odd positive integer or $$x-y=2\}$$. The minimum number of elements that must be added to the relation $$R$$, so that it is a symmetric relation, is equal to ____________.

4
JEE Main 2023 (Online) 6th April Morning Shift
Numerical
+4
-1

Let $$\mathrm{A}=\{1,2,3,4, \ldots ., 10\}$$ and $$\mathrm{B}=\{0,1,2,3,4\}$$. The number of elements in the relation $$R=\left\{(a, b) \in A \times A: 2(a-b)^{2}+3(a-b) \in B\right\}$$ is ___________.