**MCQ Questions for Class 12 Maths Chapter 1** – **Relations and functions** are provided here for the students to score good marks in the class 12 board Maths Term 1 examination. Here, all the important problems are covered as per the NCERT book. By practising and going through these MCQ questions, students can get the confidence to solve the problems easily and efficiently.

**Q.1**Let

*T*be the set of all triangles in the Euclidean plane, and let

*a*relation

*R on T*be defined as

*aRb*if

*a*is congruent to

*b*for all

*a*,

*b*$∈$

*T*. Then

*R*is :

- reflexive but not transitive
- transitive but not reflexive
- equivalence relation
- None of these

**Q.2**Consider the non-empty set consisting of children in a family and a relation

*R*defined as

*aRb*if

*a*is brother of

*b.*Then

*R*is

- symmetric but not transitive
- transitive but not symmetric
- neither symmetric nor transitive
- both symmetric and transitive

**Q.3**The maximum number of equivalence relations on the set A = [1,2,3] are

- 1
- 2
- 3
- 5

**Q.4**If a relation

*R*on the set {1,2,3} be defined by

*R*= {(1,2)}, then

*R*is

- reflexive
- transitive
- symmetric
- None of these

**Q.5**Let us define a relation

*R*in

*R*as

*aRb*if

*a*≥

*b. Then R*is

- an equivalence relation
- reflexive, transitive but not symmetric
- symmetric transitive but not reflexive
- neither transitive nor reflexive but symmetric

**Q.6**Let

*A*= [1,2,3] and consider the relation

*R*= {(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}. Then

*R*is

- reflexive but not symmetric
- reflexive but not transitive
- symmetric and transitive
- neither symmetric nor trnasitive

**Q.7**Let

*R*be the relation in the {1,2,3,4} given by

*R*= {(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)}. Choose the correct answer:

*R*is reflexive and symmetric but not transitive*R*is reflexive and transitive but not symmetric*R*is symmetric and transitive but not reflexive*R*is an equivalence relation

**Q.8**Let

*A*= [1,2,3]. Then number of relations containing (1,2) and (1,3) which are reflexive and symmetric but not transitive is

- 1
- 2
- 3
- 4

**Q.9**If the set

*A*contains 5 elements and the set

*B*contains 6 elements, then the number of one-one and onto mappings from

*A*to

*B*is

- 720
- 120
- 0
- None of these

**Q.10**Let

*A*= {1,2,3,.....

*} and*

**n***B*= {

*a, b*}. Then the number of surjections from

*A*into

*B*is:

- nP2
- 2n - 1
- 2n - 2
- None of these

**Q.11**Let f :

*R*→

*R*be defined by

*f(x)*= 1/

*x,*∀ x ∈

*R.*Then

*f*is

- one-one
- onto
- bijective
*f*is not defined

**Q.12**Which of the following functions from Z into Z are bijections?

- f(x) = x3
- f(x) = x + 2
- f(x) = 2x + 1
- f(x) = x2 + 1

**Q.13**Let

*f*:

*R*→

*R*be defined as

*f*(x) = x4. Choose the correct answer

*f*is one-one onto*f*is many-one onto*f*is one-one but not onto*f*is nether one-one nor onto

**Q.14**Let

*f : R*→

*R*be defined as

*f*(x) = 3x. Choose the correct answer.

*f*is one-one onto*f*is many-one onto*f*is one-one but not onto*f*is nether one-one nor onto

**Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.**

**(A) Both A and R are true and R is the correct explanation of A.**

**(B) Both A and R are true but R is not correct explanation of A.**

**(C) A is true but R is false.**

**(D) A is false but R is true.**

**Q.15**Let

*W*be the set of words in the English dictionary.

*A*relation

*R is defined on W*as

*R*= {(x,y) ∈

*W*X

*W*such that x and y have at least one letter in common}.

**Assertion (A) :**R is reflexive

**Reason (R) :**R is symmetric

**Q.16**Let

*R*be the relation in the set of integers Z given by

*R*= {(

*a, b) : 2 divides*a - b}.

**Assertion (A) :**R is a reflexive relation

**Reason (R) :**A relation is said to be refelexive if

*xRx,*∀ x ∈

*Z.*

**Q.17**Consider the set

*A*= (1,3,5).

**Assertion (A) :**The number of reflexive relations on set A is 29.

**Reason (R) :**A relation is said to be reflexive if

*xRx,*∀ x ∈ A

*.*

**Q.18**Consider the function

*f*:

*R*→

*R*defined as

*f*(x) = x3.

**Assertion (A) :**

*f(x)*is a one-one function.

**Reason (R) :**

*f*

*(x)*is a one-one function if co-domain = range.

**Q.19**If A = {1,2,3}, B = {4,5,6,7} and

*f*= {(1,4), (2,5), (3,6)} is a function from A to B.

**Assertion (A) :**

*f(x)*is one-one function.

**Reason (R) :**

*f(x)*is an onto function.

**Q.20**Consider the function

*f*:

*R*→

*R*defined as

*f*(x) = x/x2 + 1.

**Assertion (A) :**

*f(x)*is not one-one.

**Reason (R) :**

*f(x)*is not onto.