Introduction to Relations, Class 12 Mathematics MCQ’s

MCQ’s For All Chapters – Maths Class 12th

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

Your comments:

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)

Your comments:

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

Your comments:

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

Your comments:

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

Your comments:

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

Your comments:

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

Your comments:

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)}

Your comments:

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.

Your comments:

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}

{ }

Your comments:

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

Your comments:

Question 11 of 20

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

A

B

C

D

Your comments:

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

Your comments:

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

Your comments:

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

Your comments:

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)}

Your comments:

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

Your comments:

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

Your comments:

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

Your comments:

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,.}

Your comments:

Question 20 of 20

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