Objective Questions on Relations and Functions with Answers

Course: CBSE Class 12 Mathematics – MCQs with Answers and Explanations
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 exams standard.

1. If A has 3 elements and B has 2 elements, number of relations from A to B is

A) 6 B) 8 C) 64 D) 9

Answer: C) 64

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

2. A relation is reflexive if

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

Answer: B

Explanation: Reflexive means every element is related to itself.

3. Symmetric relation means

A) (a,b) ⇒ (b,a) B) (a,a) only C) Not reflexive D) None

Answer: A

Explanation: If (a,b)∈R then (b,a) must also belong to R.

4. Transitive relation satisfies

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

Answer: A

Explanation: Transitivity connects chained ordered pairs.

5. Equivalence relation must be

A) Reflexive only B) Symmetric only C) All three D) None

Answer: C

Explanation: Reflexive + Symmetric + Transitive.

6. Function f: A→B assigns

A) Many outputs B) One output C) No output D) Infinite outputs

Answer: B

Explanation: Each domain element has exactly one image.

7. f(x)=x³ is

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

Answer: A

Explanation: Distinct inputs give distinct cubes.

8. f(x)=x² is

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

Answer: B

Explanation: f(2)=f(−2) → same image.

9. Range of sin x is

A) R B) [−1,1] C) [0,1] D) Z

Answer: B

Explanation: Sine values lie between −1 and 1.

10. Composition fog means

A) f(g(x)) B) g(f(x)) C) f+x D) None

Answer: A

Explanation: Apply g first, then f.

11. Identity function is

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

Answer: A

Explanation: It is both one‑one and onto.

12. Inverse exists only if function is

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

Answer: B

Explanation: One‑one ensures uniqueness, onto ensures completeness.

13. Domain of √x is

A) R B) x≥0 C) x≤0 D) Z

Answer: B

Explanation: Square root defined for non‑negative values.

14. Codomain of function is decided by

A) Rule B) Definition C) Range D) Graph

Answer: B

Explanation: Codomain is fixed while defining function.

15. If f and g are onto, fog is

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

Answer: A

Explanation: Composition of onto functions remains onto.

16. Universal relation contains

A) All ordered pairs B) Identity pairs C) None D) Empty set

Answer: A

Explanation: It equals the entire Cartesian product.

17. Empty relation has

A) No elements B) All elements C) One element D) Infinite

Answer: A

Explanation: It contains no ordered pairs.

18. f(x)=|x| is

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

Answer: B

Explanation: f(2)=f(−2).

19. If A has n elements, identity relation has

A) n pairs B) n² C) 1 D) 2^n

Answer: A

Explanation: (a,a) for each element.

20. Graph of one‑one function passes

A) Vertical line test B) Horizontal line test C) Both D) None

Answer: B

Explanation: Horizontal line intersects once → injective.

Objective Questions on Relations and Functions with Answers

Objective Questions on Relations and Functions with Answers

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