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 Class 12 Maths MCQ Questions of Relations and Functions with Answers?

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 By practicing the important Class 12 Maths MCQ Questions of Relations and Functions, students can get the confidence to solve the questions easily and efficiently. Here, all the important problems are covered as per the NCERT book.

MCQ Questions for Class 12 Maths Relations and Functions with Answers are provided here for the students to get good marks within the class 12 board Maths examination. we are attending to discuss the important MCQ Questions for class 12.  Let Start Practice MCQ Questions for Class 12 Maths Relations and Functions, it covers all the concepts of relations, functions, and binary operations.

Practice MCQ Question for Class 12 Maths chapter-wise

1. The smallest integer function f(x) = [x] is

(a) One-one
(b) Many-one
(c) Both (a) & (b)
(d) None of these

2. Let R be the relation in the set (1, 2, 3, 4}, given by:
R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}.
Then:

(a) R is reflexive and symmetric but not transitive
(b) R is reflexive and transitive but not symmetric
(c) R is symmetric and transitive but not reflexive
(d) R is an equivalence relation.

3. Let R be the relation in the set N given by : R = {(a, b): a = b – 2, b > 6}. Then:

(a) (2, 4) ∈ R
(b) (3, 8) ∈ R
(c) (6, 8) ∈ R
(d) (8, 7) ∈ R.

4. Let A = {1, 2, 3}. Then number of relations containing {1, 2} and {1, 3}, which are reflexive and symmetric but not transitive is:

(a) 1
(b) 2
(c) 3
(d) 4.

5. Let A = (1, 2, 3). Then the number of equivalence relations containing (1, 2) is

(a) 1
(b) 2
(c) 3
(d) 4

6. Let f: R → R be defined as f(x) = x4. Then

(a) f is one-one onto
(b) f is many-one onto
(c) f is one-one but not onto
(d) f is neither one-one nor onto.

7. Let f : R → R be defined as f(x) = 3x. Then

(a) f is one-one onto
(b) f is many-one onto
(c) f is one-one but not onto
(d) f is neither one-one nor onto.

8. Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is

(a) Reflexive and symmetric
(b) Transitive and symmetric
(c) Equivalence
(d) Reflexive, transitive but not symmetric.

9. The function f : A → B defined by f(x) = 4x + 7, x ∈ R is

(a) one-one
(b) Many-one
(c) Odd
(d) Even

10. The function f : R → R defined by f(x) = 3 – 4x is

(a) Onto
(b) Not onto
(c) None one-one
(d) None of these

11. The number of bijective functions from set A to itself when A contains 106 elements is

(a) 106
(b) (106)2
(c) 106!
(d) 2106

12. Given set A = {a, b, c). An identity relation in set A is

(a) R = {(a, b), (a, c)}
(b) R = {(a, a), (b, b), (c, c)}
(c) R = {(a, a), (b, b), (c, c), (a, c)}
(d) R= {(c, a), (b, a), (a, a)}

13. What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A – {1, 2, 3, 4}

(a) Reflexive
(b) Transitive
(c) Symmetric
(d) None of these

14. Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is

(a) Reflexive and symmetric
(b) Transitive and symmetric
(c) Equivalence
(d) Reflexive, transitive but not symmetric.

15. Set A has 3 elements and the set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is

(a) 144
(b) 12
(c) 24
(d) 64

16. The number of binary operations that can be defined on a set of 2 elements is

(a) 8
(b) 4
(c) 16
(d) 64

17. If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C. then

(a) A = B
(b) A = C
(c) B = C
(d) A ∩ B = d

18. Let A = {1, 2}, how many binary operations can be defined on this set?

(a) 8
(b) 10
(c) 16
(d) 20

19. Let R be the relation “is congruent to” on the set of all triangles in a plane is

(a) reflexive
(b) symmetric
(c) symmetric and reflexive
(d) equivalence

20. Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is

(a) 14
(b) 16
(c) 12
(d) 8

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Answer: 

1. Answer: (b) Many-one

Explanation: We have , [1.4]=[1.6]=2

Here, two elements in A, 1.4 and 1.6 have the same image i.e., 2 in B.

Thus, f(x)=[x] is a many-one function.

2. Answer: (b) R is reflexive and transitive but not symmetric

Explanation:  Consider, A={1,2,3,4}
and R={(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)}
Clearly, R is reflexive but not symmetric as (1,2) ∈ R but (2,1) ∉ R. Also R is transitive. 

Hence, R is reflexive and transitive but not symmetric.

3. Answer: (c) (6, 8) ∈ R

4. Answer: (a) 1

Explanation: A={1,2,3}
Relation containing (1,2) and (1,3)
For symmetricity, (1,2),(2,1),(1,3) and (3,1) must be included.
For reflexivity,(1,1),(2,2),(3,3) must be included.
⇒ Only one set is there R={(1,1),(1,2),(1,3),(2,2),(2,1),(3,3),(3,1)}
⇒ Answer is 1.

5. Answer: (b) 2

Explanation: Observe that 1 is related to 2. So, we have two possible cases.

Case 1: When 1 is not related to 3, then the relation. 

R1 ={(1,1),(1,2),(2,1),(2,2),(3,3)} is the only equivalence relation containing (1,2).

Case 2: When 1 is related to 3, then A×A = {(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)} is the only equivalence relation containing (1,2)

∴ There are two required equivalence relations.

6. Answer: (d) f is neither one-one nor onto.

7. Answer: (a) f is one-one onto

8. Answer: (d) Reflexive, transitive but not symmetric

9. Answer: (a) one-one

10. Answer: (a) Onto

Explanation: Let y∈R be any real number, such that f(x)=y
∴y=3−4x

⇒4x=3−y

⇒ x = 3-y/4

So, for any real number y∈R, there exists 3-y/4 ∈ R such that f(3-y/4)=3-4(3-y/4)=3-3+y=y

Hence, f is onto.

11.  Answer: (c) 106!

For a finite set S, there is a bijection between the set of possible total orderings of the elements and the set of bijections from S to S. That is to say, the number of permutations of elements of S is the same as the number of total orderings of that set, i.e. n!. 

We have the set A that contains 106 elements, so the number of bijective functions from set A to itself is 106!.

12. Answer: (b) R = {(a, a), (b, b), (c, c)}

13. Answer: (d) None of these

14. Answer: (b) Transitive and symmetric

15. Answer: (c) 24

Explanation: To define the injective functions from set A to set B, we can map the first element of set A to any of the 4 elements of set B.
Then the second element can not be mapped to the same element of set A, hence, there are 3 choices in set B for the second element of set A.
Similarly, there are 2 choices in set B for the third element of set A.
Hence the total number of injective functions are 4×3×2=24

16. Answer: (c) 16

Explanation: The number of binary operations on a set consisting of n elements \(=n^{n^2}\)

∴ Required no. of binary operations \(=2^{2^2}=16\)

17. Answer: (c) B = C

Explanation: Let x∈C
Suppose x∈A⇒x∈A∩C
⇒x∈A∩B(∵A∩C=A∩B)
Thus x∈B
Again suppose x∉ A⇒x∈C∪A
⇒x∈B∪A⇒x∈B
Hence C⊆B .......(1)
Similarly, we can show that B⊆C .....(2)
Combining (1) and (2) we get B=C

18. Answer: (c) 16

19. Answer: (d) equivalence

20. Answer: (a) 14

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