Introduction to Relations, Class 12 Mathematics NCERT Solutions

1. There will be total 20 MCQ in this test.
2. Please keep a pen and paper ready for rough work but keep your books away.
3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number.
4. No negative marking for incorrect choice.
5. Please click on “Finish the Test” when you want to exit.
6. All the best – Happy Studying

1. Let R = { (P,Q) : OP = OQ , O being the origin} be an equivalence relation on A . The equivalence class [( 1,2)] is

 A

 B

 C

 D

Question 1 of 20

2. Let a relation T on the set R of real numbers be
T = { (a,b) : 1 + ab < 0, a,R}. Then from among the ordered pairs (1,1) (1,2)(1,-2)(2,2), the only pair that belongs to T is________.

 (2,2),

 (1,1),

 (1,-2)

 (1,2)

Question 2 of 20

3. For real number x and y, we write is an irrational number. Then the relation R is:

 Reflexive

 Symmetric

 Transitive

 Equivalence

Question 3 of 20

4. Let A = {1, 2, 3, 4} and let R = {(2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then, R is

  Symmetric

 Transitive

 Reflexive

  Equivalence relation

Question 4 of 20

5. If A = {1,3,5,7} and we define a relation Then the number of elements in the relation R is

 2

 1

 3

 0

Question 5 of 20

6. If A = {1,3,5,7} and define a relation, such that R =

{ (a,b) a,b A : |a+b| = 8}. Then how many elements are there in the relation R

 8

 16

 1

 4

Question 6 of 20

7. In the set  the relation R is defined by (a, b) R (c, d)  ad = bc. Then R is

  symmetric and transitive but not reflexive

 reflexive and transitive but not symmetric

 Equivalence relation

 Partial order relation

Question 7 of 20

8. If A = {1, 2, 3, 4} and B = {1, 3, 5} and R is a relation from A to B defined by

(a, b) element of R  a < b. Then, R = ?

  {(2, 3), (4, 5), (1, 3), (2, 5)}

  {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

 {(2, 3), (4, 5), (1, 3), (2, 5), (5, 3)}

  {(5, 3), (3, 5), (5, 4), (4, 5)}

Question 8 of 20

9. Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R is

 R is reflexive and symmetric but not transitive.

  R is symmetric and transitive but not reflexive.

 R is an equivalence relation.

 R is reflexive and transitive but not symmetric.

Question 9 of 20

10. Let A = {1,2,3,4,5,6,7}. P={1,2}, Q = {3, 7}. Write the elements of the set R so that P, Q and R form a partition that results in equivalence relation.

  {4,5,6}

 {0}

  {1,2,3,4,5,6,7}

 { }

Question 10 of 20

11. Let R be a relation on set A of triangles in a plane.

R = { (T1 , T2) : T1 , T2element ofA and T1 is congruent to T2} Then the relation R is______

 Equivalence relation

 Transitive

 Symmetric

  Reflexive

Question 11 of 20

12. Which one of the following relations on set of real numbers is an equivalence relation?

 A

 B

 C

 D

Question 12 of 20

13. Let C = {(a, b): a² + b² = 1; a, b R} a relation on R, set of real numbers. Then C is

 Equivalence relation

  Reflexive

 Transitive

 Symmetric

Question 13 of 20

14. Let A = {1,2,3,4} and B = { x,y,z}. Then R = {(1,x) , ( 2,z), (1,y), (3,x)} is

 relation from B to A

 Is not a relation

 relation from A to B

 relation from B to B

Question 14 of 20

15. Let R be a relation on N, set of natural numbers such that m R n m divides n. Then R is

 Reflexive and symmetric

  Neither reflexive nor transitive

 Reflexive and transitive

 Symmetric and transitive

Question 15 of 20

16. If R be a relation “less than” from set A = {1, 2, 3, 4} to B = {1, 3, 5}, i.e.

(a, b) R if a < b, if (b,a)  R^-1elements in R^-1 are

  {(3, 3), (3, 5), (5, 3), (5, 5)}

 {(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}

  {(3, 3), (3, 4), (4, 5)}

  {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

Question 16 of 20

17. Let R be a relation on a finite set A having n elements. Then, the number of relations on A is

 n x n

 2ⁿ

 n²

 2^nxn

Question 17 of 20

18. Let R be a relation on N (set of natural numbers)
such that (m, n) R (p, q)mq(n + p) = np(m + q). Then, R is

 An Equivalence Relation

 Only Reflexive

 Symmetric and reflexive.

 Only Transitive

Question 18 of 20

19. Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. Then, R is

  Symmetric only

 An equivalence relation

 Reflexive and symmetric only

 Reflexive and transitive only

Question 19 of 20

20. Let R be an equivalence relation on Z, the set of integers.

R = { (a,b): a,bZ and a – b is a multiple of 3 } The Equivalence class of [1] is

 {..-7,-4,2,5,8,.}

  {.-4,-1,2,5,8,.}

  {.-4,-1,2,5,8,.}

 {…..-5,-2,1,4,7,.}

Question 20 of 20

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