Class 12 Maths Relations & Functions Chapter-Wise MCQs

Class 12 Maths Relations & Functions Chapter‑Wise MCQs

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. Cartesian product A×B contains

A) Only common elements B) Ordered pairs C) Functions D) Relations only

Answer: B

Explanation: A×B consists of all ordered pairs (a,b) where a∈A and b∈B.

2. If n(A)=2, number of elements in A×A is

A) 2 B) 4 C) 8 D) 16

Answer: B

Explanation: n(A×A)=n(A)²=2²=4.

3. Relation R={(1,1),(2,2)} is

A) Symmetric B) Identity C) Transitive D) All

Answer: D

Explanation: Identity relation satisfies reflexive, symmetric, transitive properties.

4. Domain of log x is

A) x>0 B) x≥0 C) R D) Z

Answer: A

Explanation: Logarithm defined only for positive numbers.

5. Range of cos x is

A) [−1,1] B) [0,1] C) R D) Z

Answer: A

Explanation: Cosine values lie between −1 and 1.

6. f(x)=2x+3 is

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

Answer: A

Explanation: Linear functions with non‑zero slope are injective.

7. If f is bijective, inverse is

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

Answer: A

Explanation: Bijective functions always possess inverse functions.

8. f(x)=|x| is not one‑one because

A) Same output for different inputs B) Undefined C) Constant D) None

Answer: A

Explanation: f(2)=f(−2).

9. Onto function covers

A) Domain B) Codomain C) Range only D) None

Answer: B

Explanation: Every element of codomain has pre‑image.

10. Composition of functions is associative

A) True B) False C) Sometimes D) None

Answer: A

Explanation: (f∘g)∘h = f∘(g∘h).

11. Smallest relation in A×A is

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

Answer: C

Explanation: Empty set has no ordered pairs.

12. Largest relation in A×A is

A) Universal B) Identity C) Empty D) Symmetric

Answer: A

Explanation: Universal relation = entire Cartesian product.

13. Number of functions from A to B is

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

Answer: B

Explanation: If n(A)=m, n(B)=n → n^m functions.

14. Identity function is

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

Answer: A

Explanation: It is both injective and surjective.

15. If f and g are bijective, fog is

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

Answer: A

Explanation: Composition of bijective functions remains bijective.

16. Graph test for function is

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

Answer: A

Explanation: Vertical line must intersect once.

17. Horizontal line test checks

A) Onto B) One‑one C) Constant D) Domain

Answer: B

Explanation: Determines injectivity.

18. Range of exponential function is

A) x>0 B) R C) Z D) x≥0

Answer: A

Explanation: e^x always positive.

19. Equivalence class forms

A) Partition B) Function C) Domain D) Graph

Answer: A

Explanation: Equivalence relation partitions set.

20. If function has inverse, it is

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

Answer: A

Explanation: Only bijective functions are invertible.

Class 12 Maths Relations & Functions Chapter-Wise MCQs

Class 12 Maths Relations & Functions Chapter‑Wise MCQs

Login with your site account

Register a new account

Search

Modal title