Question:
The region R on the set \(A=\{x \in Z:0\leq x\leq 12\}\) , given by \(R=\{(a,b):|a-b|\) is a multiple of 4 \(\}\) is :
The region R on the set \(A=\{x \in Z:0\leq x\leq 12\}\) , given by \(R=\{(a,b):|a-b|\) is a multiple of 4 \(\}\) is :
Updated On: May 21, 2024
- Reflexive but not Symmetric
- Reflexive but not Transitive
- Symmetric but not Transitive
- Equivalence relation
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct option is (D): Equivalence relation
Was this answer helpful?
0
0
Top Questions on Relations and functions
- Let \[ L_1 : \frac{x-1}{1} = \frac{y-2}{-1} = \frac{z-1}{-1} \quad {and} \quad L_2 : \frac{x+1}{1} = \frac{y-2}{2} = \frac{z-2}{2} \] be two lines. Let \( L_3 \) be a line passing through the point \( (\alpha, \beta, \gamma) \) and be perpendicular to both \( L_1 \) and \( L_2 \). If \( L_3 \) intersects \( L_1 \) where \( 5x - 11y - 8z = 1 \), then \( 5x - 11y - 8z \) equals:
- JEE Main - 2025
- Mathematics
- Relations and functions
- Let the position vectors of three vertices of a triangle be \( \overrightarrow{p} = 4\hat{i} + \hat{j} - 3\hat{k} \), \( \overrightarrow{q} = -5\hat{i} + 2\hat{j} + 3\hat{k} \), and \( \overrightarrow{r} = -5\hat{i} + 3\hat{j} + 2\hat{k} \). Then \( \alpha + 2\beta + 5\gamma \) is equal to:
- JEE Main - 2025
- Mathematics
- Relations and functions
- Let the range of the function \[ f(x) = 6 + 16 \cos x \cdot \cos\left(\frac{\pi}{3} - x\right) \cdot \cos\left(\frac{\pi}{3} + x\right) \cdot \sin 3x \cdot \cos 6x, \quad x \in R \text{ be } [\alpha, \beta]. \] Then the distance of the point \((\alpha, \beta)\) from the line \(3x + 4y + 12 = 0\) is:
- JEE Main - 2025
- Mathematics
- Relations and functions
- The relation \( R = \{(x, y) : x, y \in \mathbb{Z} \text{ and } x + y \text{ is even} \} \) is:
- JEE Main - 2025
- Mathematics
- Relations and functions
- Let the position vectors of three vertices of a triangle be \( \overrightarrow{p} = 4\hat{i} + \hat{j} - 3\hat{k} \), \( \overrightarrow{q} = -5\hat{i} + 2\hat{j} + 3\hat{k} \), and \( \overrightarrow{r} = -5\hat{i} + 3\hat{j} + 2\hat{k} \). Then \( \alpha + 2\beta + 5\gamma \) is equal to:
- JEE Main - 2025
- Mathematics
- Relations and functions
View More Questions
Questions Asked in CUET exam
- From the given options, which pass connects Jammu with Srinagar?
- CUET (UG) - 2024
- Static GK
- The corner points of the feasible region determined by $x + y \leq 8$, $2x + y \geq 8$, $x \geq 0$, $y \geq 0$ are $A(0, 8)$, $B(4, 0)$, and $C(8, 0)$. If the objective function $Z = ax + by$ has its maximum value on the line segment $AB$, then the relation between $a$ and $b$ is:
- CUET (UG) - 2024
- Linear Programmig Problem
- Match the words in List-I with their definitions in List-II :
List-I (Words) List-II (Definitions) (A) Theocracy (I) One who keeps drugs for sale and puts up prescriptions (B) Megalomania (II) One who collects and studies objects or artistic works from the distant past (C) Apothecary (III) A government by divine guidance or religious leaders (D) Antiquarian (IV) A morbid delusion of one’s power, importance or godliness Choose the correct answer from the options given below :- CUET (UG) - 2024
- Vocabulary
- Complete the sentences given in List-I with the appropriate prepositions given in List-II:
- Identify the correct sequence of the Selection process:
(A) Selection decision
(B) Employment interview
(C) Selection tests
(D) Reference checking- CUET (UG) - 2024
- Staffing
View More Questions