CBSE Board Exam MCQs – Relations and Functions

Class: CBSE Class 12 Mathematics
Subject: Mathematics
Section: Relations and Functions
Topic: CBSE Board Exam MCQs – 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 on set A is symmetric if:

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

Answer: B
Explanation: Symmetric relation means if one ordered pair exists, its reverse must also exist.

Q2. A transitive relation satisfies:

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

Answer: C
Explanation: Transitivity connects chained relations into a direct relation.

Q3. Number of relations on a set having 3 elements:

A. 9
B. 27
C. 512
D. 64

Answer: C
Explanation: Relations = 2^(n²) = 2⁹ = 512.

Q4. Identity relation contains:

A. All ordered pairs
B. Only (a,a)
C. No pairs
D. Symmetric pairs

Answer: B
Explanation: Identity relation maps each element to itself.

Q5. A function is onto if:

A. Every domain element has image
B. Every codomain element has pre‑image
C. Images repeat
D. None

Answer: B
Explanation: Onto ensures codomain = range.

Q6. One‑one function means:

A. Same image allowed
B. Distinct images for distinct inputs
C. Constant output
D. Onto only

Answer: B
Explanation: Injective mapping preserves uniqueness.

Q7. Bijective function is:

A. One‑one only
B. Onto only
C. Both one‑one & onto
D. Many‑one

Answer: C
Explanation: Required for invertibility.

Q8. Inverse exists only when function is:

A. Onto
B. One‑one
C. Bijective
D. Constant

Answer: C
Explanation: Both injective & surjective required.

Q9. f(x)=x³ is:

A. Bijective on R
B. Many‑one
C. Not onto
D. Constant

Answer: A
Explanation: Strictly increasing → one‑one & onto on R.

Q10. f(x)=|x| on R is:

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

Answer: B
Explanation: f(2)=f(‑2).

Q11. Empty relation is:

A. Reflexive
B. Symmetric
C. Transitive
D. All

Answer: D
Explanation: Vacuously satisfies all properties.

Q12. Universal relation is:

A. Subset of A×A
B. Equal to A×A
C. Identity
D. Empty

Answer: B
Explanation: Contains all ordered pairs.

Q13. Equivalence relation forms:

A. Functions
B. Classes
C. Domains
D. Graphs

Answer: B
Explanation: Called equivalence classes.

Q14. Number of functions A(3)→B(2):

A. 6
B. 8
C. 9
D. 27

Answer: B
Explanation: 2³ = 8.

Q15. Constant function is:

A. Injective
B. Many‑one
C. Onto
D. Bijective

Answer: B
Explanation: All inputs share same output.

Q16. Identity function is always:

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

Answer: A
Explanation: Perfect one‑one & onto mapping.

Q17. Range of onto function equals:

A. Domain
B. Codomain
C. Image set subset
D. None

Answer: B
Explanation: By definition of surjection.

Q18. Many‑one onto function is:

A. Possible
B. Impossible
C. Identity
D. Bijective

Answer: A
Explanation: Multiple inputs can map to full codomain.

Q19. If f has inverse, f⁻¹ is:

A. Function
B. Relation only
C. Constant
D. None

Answer: A
Explanation: Inverse of bijection is function.

Q20. Relation from A to B is subset of:

A. A+B
B. A×B
C. B×A
D. A²

Answer: B
Explanation: Defined using Cartesian product.

CBSE Board Exam MCQs – Relations and Functions

CBSE Board Exam MCQs – Relations and Functions

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