Relations and Types of Relation
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Sets, Relation and Function

116837 Let the relation \(\rho\) be defined on \(R\) as apb if \(1+\) \(\mathbf{a b}>\mathbf{0}\). Then

1 \(\rho\) is reflexive only.
2 \(\rho\) is equivalence relation.
3 \(\rho\) is reflexive and transitive but not symmetric
4 \(\rho\) is reflexive and symmetric but not transitive.
WB JEE-2019
Sets, Relation and Function

116838 Let \(A=\{2,3,4,5, \ldots .30\}\) and ' \(\simeq\) ' be an equivalence relation on \(A \times A\), defined by \((a, b)\) \(\simeq(c, d)\), if and only if ad = bc. Then, the number of ordered pairs, which satisfy this equivalence relation with ordered pair \((4,3)\) is equal to

1 5
2 6
3 8
4 7
JEE Main 16.03.2021 Shift-II
Sets, Relation and Function

116839 Let \(\mathbf{R}=\{(\mathbf{P}, \mathbf{Q}) \mid, \mathbf{P}\) and \(\mathbf{Q}\) are at the same distance from the origin \(\}\) be a relation, then the equivalence class of \((1,-1)\) is the set

1 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=4\right\}\)
2 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=1\right\}\)
3 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=\sqrt{2}\right\}\)
4 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=2\right\}\)
JEE Main 26.02.2021 Shift-I
Sets, Relation and Function

116840 Which of the following is not correct for relation \(R\) on the set of real numbers?

1 \((x, y) \in R \Leftrightarrow 0\lt |x|-|y| \leq 1\) is neither transitive nor symmetric.
2 \((x, y) \in R \Leftrightarrow 0\lt |x-y| \leq 1\) is symmetric and transitive.
3 \((x, y) \in R \Leftrightarrow|x|-|y| \leq 1\) is reflexive but not symmetric
4 \((\mathrm{x}, \mathrm{y}) \in \mathrm{R} \Leftrightarrow|\mathrm{x}-\mathrm{y}| \leq 1\) is reflexive and symmetric.
JEE Main 31.08.2021 Shift-I
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Sets, Relation and Function

116837 Let the relation \(\rho\) be defined on \(R\) as apb if \(1+\) \(\mathbf{a b}>\mathbf{0}\). Then

1 \(\rho\) is reflexive only.
2 \(\rho\) is equivalence relation.
3 \(\rho\) is reflexive and transitive but not symmetric
4 \(\rho\) is reflexive and symmetric but not transitive.
WB JEE-2019
Sets, Relation and Function

116838 Let \(A=\{2,3,4,5, \ldots .30\}\) and ' \(\simeq\) ' be an equivalence relation on \(A \times A\), defined by \((a, b)\) \(\simeq(c, d)\), if and only if ad = bc. Then, the number of ordered pairs, which satisfy this equivalence relation with ordered pair \((4,3)\) is equal to

1 5
2 6
3 8
4 7
JEE Main 16.03.2021 Shift-II
Sets, Relation and Function

116839 Let \(\mathbf{R}=\{(\mathbf{P}, \mathbf{Q}) \mid, \mathbf{P}\) and \(\mathbf{Q}\) are at the same distance from the origin \(\}\) be a relation, then the equivalence class of \((1,-1)\) is the set

1 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=4\right\}\)
2 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=1\right\}\)
3 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=\sqrt{2}\right\}\)
4 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=2\right\}\)
JEE Main 26.02.2021 Shift-I
Sets, Relation and Function

116840 Which of the following is not correct for relation \(R\) on the set of real numbers?

1 \((x, y) \in R \Leftrightarrow 0\lt |x|-|y| \leq 1\) is neither transitive nor symmetric.
2 \((x, y) \in R \Leftrightarrow 0\lt |x-y| \leq 1\) is symmetric and transitive.
3 \((x, y) \in R \Leftrightarrow|x|-|y| \leq 1\) is reflexive but not symmetric
4 \((\mathrm{x}, \mathrm{y}) \in \mathrm{R} \Leftrightarrow|\mathrm{x}-\mathrm{y}| \leq 1\) is reflexive and symmetric.
JEE Main 31.08.2021 Shift-I
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Sets, Relation and Function

116837 Let the relation \(\rho\) be defined on \(R\) as apb if \(1+\) \(\mathbf{a b}>\mathbf{0}\). Then

1 \(\rho\) is reflexive only.
2 \(\rho\) is equivalence relation.
3 \(\rho\) is reflexive and transitive but not symmetric
4 \(\rho\) is reflexive and symmetric but not transitive.
WB JEE-2019
Sets, Relation and Function

116838 Let \(A=\{2,3,4,5, \ldots .30\}\) and ' \(\simeq\) ' be an equivalence relation on \(A \times A\), defined by \((a, b)\) \(\simeq(c, d)\), if and only if ad = bc. Then, the number of ordered pairs, which satisfy this equivalence relation with ordered pair \((4,3)\) is equal to

1 5
2 6
3 8
4 7
JEE Main 16.03.2021 Shift-II
Sets, Relation and Function

116839 Let \(\mathbf{R}=\{(\mathbf{P}, \mathbf{Q}) \mid, \mathbf{P}\) and \(\mathbf{Q}\) are at the same distance from the origin \(\}\) be a relation, then the equivalence class of \((1,-1)\) is the set

1 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=4\right\}\)
2 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=1\right\}\)
3 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=\sqrt{2}\right\}\)
4 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=2\right\}\)
JEE Main 26.02.2021 Shift-I
Sets, Relation and Function

116840 Which of the following is not correct for relation \(R\) on the set of real numbers?

1 \((x, y) \in R \Leftrightarrow 0\lt |x|-|y| \leq 1\) is neither transitive nor symmetric.
2 \((x, y) \in R \Leftrightarrow 0\lt |x-y| \leq 1\) is symmetric and transitive.
3 \((x, y) \in R \Leftrightarrow|x|-|y| \leq 1\) is reflexive but not symmetric
4 \((\mathrm{x}, \mathrm{y}) \in \mathrm{R} \Leftrightarrow|\mathrm{x}-\mathrm{y}| \leq 1\) is reflexive and symmetric.
JEE Main 31.08.2021 Shift-I
For More Updates join with Us
Sets, Relation and Function

116837 Let the relation \(\rho\) be defined on \(R\) as apb if \(1+\) \(\mathbf{a b}>\mathbf{0}\). Then

1 \(\rho\) is reflexive only.
2 \(\rho\) is equivalence relation.
3 \(\rho\) is reflexive and transitive but not symmetric
4 \(\rho\) is reflexive and symmetric but not transitive.
WB JEE-2019
Sets, Relation and Function

116838 Let \(A=\{2,3,4,5, \ldots .30\}\) and ' \(\simeq\) ' be an equivalence relation on \(A \times A\), defined by \((a, b)\) \(\simeq(c, d)\), if and only if ad = bc. Then, the number of ordered pairs, which satisfy this equivalence relation with ordered pair \((4,3)\) is equal to

1 5
2 6
3 8
4 7
JEE Main 16.03.2021 Shift-II
Sets, Relation and Function

116839 Let \(\mathbf{R}=\{(\mathbf{P}, \mathbf{Q}) \mid, \mathbf{P}\) and \(\mathbf{Q}\) are at the same distance from the origin \(\}\) be a relation, then the equivalence class of \((1,-1)\) is the set

1 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=4\right\}\)
2 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=1\right\}\)
3 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=\sqrt{2}\right\}\)
4 \(\mathrm{S}=\left\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}^2+\mathrm{y}^2=2\right\}\)
JEE Main 26.02.2021 Shift-I
Sets, Relation and Function

116840 Which of the following is not correct for relation \(R\) on the set of real numbers?

1 \((x, y) \in R \Leftrightarrow 0\lt |x|-|y| \leq 1\) is neither transitive nor symmetric.
2 \((x, y) \in R \Leftrightarrow 0\lt |x-y| \leq 1\) is symmetric and transitive.
3 \((x, y) \in R \Leftrightarrow|x|-|y| \leq 1\) is reflexive but not symmetric
4 \((\mathrm{x}, \mathrm{y}) \in \mathrm{R} \Leftrightarrow|\mathrm{x}-\mathrm{y}| \leq 1\) is reflexive and symmetric.
JEE Main 31.08.2021 Shift-I
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