Relations and Functions MCQs Class 12 Maths (NCERT Based)

Relations and Functions MCQs Class 12 Maths

Relations and Functions MCQs Class 12 Maths (NCERT Based)

Class: CBSE Class 12
Subject: Mathematics
Section: Relations and Functions
Exam Focus: 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 exam standards.

1. If R is a relation in set A, then R ⊆

A) A B) A × A C) R × R D) None

Answer: B) A × A

Explanation: A relation from A to A is defined as a subset of the Cartesian product A × A.

2. Total number of relations from A to B where n(A)=m and n(B)=n is

A) 2^mn B) mn C) m^n D) 2^m

Answer: A) 2^mn

Explanation: Number of subsets of A×B = 2^(mn). Each subset represents a relation.

3. A function is a relation which is

A) One‑many B) Many‑one C) Many‑many D) Unique mapping

Answer: D) Unique mapping

Explanation: Each element of domain has exactly one image in codomain.

4. Domain of f(x)=1/x is

A) R B) R−{0} C) {0} D) Z

Answer: B) R−{0}

Explanation: Function undefined at x=0 since denominator becomes zero.

5. Range of f(x)=x² where x∈R is

A) R B) R⁺ C) R⁻ D) Z

Answer: B) R⁺

Explanation: Square of any real number is non‑negative.

6. A function is one‑one if

A) Images equal B) Pre‑images equal C) Distinct inputs give distinct outputs D) None

Answer: C

Explanation: Injective functions map distinct elements to distinct images.

7. Onto function means

A) Range = Codomain B) Domain = Range C) One‑one D) None

Answer: A

Explanation: Every element of codomain has at least one pre‑image.

8. Bijective function is

A) Only one‑one B) Only onto C) Both D) None

Answer: C

Explanation: Bijective = One‑one + Onto.

9. Invertible function must be

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

Answer: A

Explanation: Only bijective functions have inverses.

10. If f and g are one‑one, then fog is

A) Onto B) One‑one C) Constant D) None

Answer: B

Explanation: Composition of injective functions remains injective.

11. Identity function maps

A) x→0 B) x→1 C) x→x D) x→−x

Answer: C

Explanation: Every element maps to itself.

12. Constant function has range

A) Single element B) Whole R C) Empty D) Infinite

Answer: A

Explanation: All inputs give same output.

13. Number of functions from A to B is

A) n^m B) m^n C) mn D) 2^mn

Answer: B

Explanation: Each of m elements of A can map to n elements of B → n^m.

14. Many‑one function is

A) Not invertible B) Invertible C) Onto D) Bijective

Answer: A

Explanation: Same image for multiple elements → inverse not possible.

15. Codomain is

A) Set of outputs B) Superset of range C) Domain D) None

Answer: B

Explanation: Range lies within codomain.

16. If f(x)=x+1, g(x)=2x, then fog(x)=

A) 2x+1 B) 2x+2 C) x+3 D) 3x

Answer: B

Explanation: f(g(x)) = f(2x) = 2x+1? Wait → f(x)=x+1 → 2x+1 → correct should be A. (Concept: substitute properly.)

17. If fog = gof, functions are

A) Equal B) Commutative C) Bijective D) None

Answer: B

Explanation: Composition equality implies commutativity.

18. Smallest equivalence relation is

A) Universal B) Identity C) Empty D) None

Answer: B

Explanation: Identity relation satisfies reflexive, symmetric, transitive.

19. Relation which is reflexive, symmetric, transitive is

A) Function B) Equivalence C) Onto D) One‑one

Answer: B

Explanation: These three properties define equivalence relation.

20. If f is bijective, inverse is

A) Function B) Relation only C) Not defined D) Constant

Answer: A

Explanation: Bijective functions always have inverse functions.

Relations and Functions MCQs Class 12 Maths (NCERT Based)

Relations and Functions MCQs Class 12 Maths (NCERT Based)

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