Relations & Functions Class 11 MCQs with Answers (Chapter-Wise NCERT)

Relations & Functions Class 11 MCQs

Relations & Functions Class 11 MCQs with Answers

Class: 11 | Subject: Mathematics | Section: Sets & Functions
Topic: Chapter‑Wise NCERT Practice Questions
Aligned with CBSE Board Examination Standard

Instructions: These Multiple Choice Questions (MCQs) are designed strictly as per the NCERT syllabus, making them ideal for CBSE Class 11 Board Examination practice. Each question includes a detailed concept‑clearing explanation.

1. A relation from A to B is a subset of:

A) A ∪ B
B) A × B
C) B × A
D) Power set

Answer: B) A × B
Explanation: Any relation is defined as a subset of the Cartesian product A × B.

2. If A has m elements and B has n elements, then A × B has:

A) m+n
B) mn
C) m²
D) n²

Answer: B) mn
Explanation: Each element of A pairs with every element of B.

3. A relation in A is called reflexive if:

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

Answer: B
Explanation: Every element must relate to itself.

4. Symmetric relation means:

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

Answer: A
Explanation: If a is related to b, then b is related to a.

5. Transitive relation satisfies:

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

Answer: A
Explanation: Relation continues through elements.

6. A function is a relation in which:

A) One input has many outputs
B) Every input has exactly one output
C) Outputs repeat
D) None

Answer: B
Explanation: This is the defining property of a function.

7. Domain of a function refers to:

A) Outputs
B) Inputs
C) Range
D) Graph

Answer: B
Explanation: All permissible input values.

8. Range is:

A) All inputs
B) All outputs obtained
C) Cartesian product
D) Relation

Answer: B
Explanation: Actual outputs corresponding to domain.

9. Codomain is:

A) Set of inputs
B) Set where outputs lie
C) Range only
D) Subset

Answer: B
Explanation: It contains all possible outputs.

10. One‑one function means:

A) Different inputs → different outputs
B) Same outputs allowed
C) Many outputs
D) None

Answer: A
Explanation: Injective mapping.

11. Onto function means:

A) Range = Codomain
B) Domain = Range
C) Many outputs
D) None

Answer: A
Explanation: Every codomain element has pre‑image.

12. Many‑one function allows:

A) Many inputs same output
B) One input many outputs
C) Both
D) None

Answer: A
Explanation: Valid function type.

13. Identity function is defined as:

A) f(x)=0
B) f(x)=x
C) f(x)=1
D) f(x)=x²

Answer: B
Explanation: Every element maps to itself.

14. Constant function example:

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

Answer: B
Explanation: Output same for all inputs.

15. Total functions from A(2 elements) to B(3 elements):

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

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

16. Graph of a function passes vertical line test:

A) Always
B) Never
C) Sometimes
D) None

Answer: A
Explanation: Each x has one y.

17. Relation can have:

A) Multiple outputs per input
B) One output only
C) No ordered pairs
D) None

Answer: A
Explanation: Unlike functions.

18. If f(x)=x², domain in R is:

A) Positive only
B) All real numbers
C) Integers
D) Natural numbers

Answer: B
Explanation: Square defined for all reals.

19. Range of f(x)=x² in R:

A) R
B) Positive reals incl. 0
C) Negative reals
D) Integers

Answer: B
Explanation: Squares are non‑negative.

20. Function mapping each student to roll number is:

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

Answer: B
Explanation: Unique roll number for each student.

Relations & Functions Class 11 MCQs with Answers (Chapter-Wise NCERT)

Relations & Functions Class 11 MCQs with Answers

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