1
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 ____________.
2
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 __________

3
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 __________.

4
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 _________.