Important MCQs on Types of Relations and Functions

Class: CBSE Class 12 Mathematics
Subject: Mathematics
Section: Relations and Functions
Topic: Types of Relations and Functions
Board: CBSE Board Examinations

Instructions: These Multiple Choice Questions (MCQs) are designed strictly as per the NCERT syllabus, making them ideal for CBSE Class 12 Board Examination standard practice.

Q1. A relation R in a set A is called reflexive if:

A. (a,b) ∈ R ⇒ (b,a) ∈ R
B. (a,a) ∈ R for all a ∈ A
C. (a,b) and (b,c) ∈ R ⇒ (a,c) ∈ R
D. None

Answer: B
Explanation: Reflexive relation means every element is related to itself. Hence (a,a) must belong to R for all elements.

Q2. A relation which is reflexive, symmetric and transitive is called:

A. Universal relation
B. Identity relation
C. Equivalence relation
D. Empty relation

Answer: C
Explanation: Equivalence relation satisfies all three properties: reflexive, symmetric and transitive.

Q3. If R={(1,1),(2,2),(3,3)} on A={1,2,3}, then R is:

A. Identity relation
B. Empty relation
C. Symmetric only
D. Not reflexive

Answer: A
Explanation: Identity relation contains only ordered pairs of type (a,a).

Q4. Total number of relations from A to B if n(A)=2, n(B)=3:

A. 6
B. 8
C. 64
D. 32

Answer: C
Explanation: Number of relations = 2^(mn) = 2^(2×3)=2^6=64.

Q5. Every function is a relation but every relation is not a function because:

A. Function may not have domain
B. Relation may assign multiple images
C. Function has no codomain
D. None

Answer: B
Explanation: In a function, each element has exactly one image. Relations may have many.

Q6. One–one function is also called:

A. Onto
B. Injective
C. Surjective
D. Constant

Answer: B
Explanation: Injective means distinct elements have distinct images.

Q7. Onto function is also called:

A. Surjective
B. Injective
C. Identity
D. Many–one

Answer: A
Explanation: Onto means every element of codomain has a pre‑image.

Q8. f(x)=x² from R→R is:

A. One–one
B. Onto
C. Many–one
D. Bijective

Answer: C
Explanation: f(2)=f(-2)=4, hence many–one and not onto in R.

Q9. A bijective function is both:

A. Injective & Surjective
B. Many–one & Onto
C. Constant & Onto
D. None

Answer: A
Explanation: Bijective = One–one + Onto.

Q10. Invertible function must be:

A. Many–one
B. Bijective
C. Onto only
D. Constant

Answer: B
Explanation: Only bijective functions possess inverse.

Q11. Symmetric relation means:

A. (a,b) ⇒ (b,a)
B. (a,a)
C. Transitive
D. None

Answer: A
Explanation: Order reversal property defines symmetry.

Q12. Transitive relation property:

A. (a,b),(b,c) ⇒ (a,c)
B. (b,a)
C. (a,a)
D. None

Answer: A
Explanation: Chain relation leads to direct relation.

Q13. Constant function example:

A. f(x)=x
B. f(x)=5
C. f(x)=x²
D. f(x)=1/x

Answer: B
Explanation: Same output for all inputs.

Q14. Identity function:

A. f(x)=0
B. f(x)=x
C. f(x)=x²
D. f(x)=|x|

Answer: B
Explanation: Output equals input.

Q15. f:N→N, f(x)=x+1 is:

A. Onto
B. One–one not onto
C. Bijective
D. Constant

Answer: B
Explanation: 1 has no pre‑image.

Q16. Number of functions from A(2) to B(3):

A. 6
B. 9
C. 8
D. 3

Answer: B
Explanation: n(B)^(n(A)) = 3²=9.

Q17. Empty relation contains:

A. All pairs
B. No pair
C. Identity pairs
D. Symmetric pairs

Answer: B
Explanation: Null set relation.

Q18. Universal relation contains:

A. No pairs
B. All possible pairs
C. Identity only
D. None

Answer: B
Explanation: Cartesian product itself.

Q19. If f has inverse, it is:

A. Bijective
B. Many–one
C. Constant
D. None

Answer: A
Explanation: Invertibility requires one–one & onto.

Q20. Equivalence relation partitions set into:

A. Subsets
B. Equivalent classes
C. Domains
D. Functions

Answer: B
Explanation: Each class contains mutually related elements.

Important MCQs on Types of Relations and Functions

Important MCQs on Types of Relations and Functions

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