Objective Questions on Types of Functions Class 11 Mathematics

Objective Questions on Types of Functions Class 11

Objective Questions on Types of Functions Class 11 Mathematics

Class: 11 | Subject: Mathematics | Section: Sets & Functions
Topic: Types of Functions – NCERT Based MCQs
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 function f: A → B is one‑one if:

A) f(a₁)=f(a₂) ⇒ a₁=a₂
B) Every element has image
C) Range = Domain
D) None

Answer: A
Explanation: Distinct inputs must have distinct outputs.

2. Onto function means:

A) Range ⊂ Codomain
B) Range = Codomain
C) Domain = Range
D) None

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

3. Many‑one function allows:

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

Answer: B
Explanation: Multiple inputs may share same output.

4. One‑one and onto function is called:

A) Identity
B) Bijective
C) Constant
D) Polynomial

Answer: B
Explanation: Injective + Surjective.

5. Identity function is:

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

Answer: B
Explanation: Maps every element to itself.

6. Constant function has:

A) Same output
B) Same input
C) Increasing graph
D) None

Answer: A
Explanation: Output independent of input.

7. f(x)=x² is:

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

Answer: B
Explanation: x and −x give same output.

8. f(x)=x³ is:

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

Answer: A
Explanation: Distinct inputs → distinct outputs.

9. Onto function graph touches:

A) All x values
B) All y values of codomain
C) Origin only
D) None

Answer: B
Explanation: Covers entire codomain.

10. Bijective functions have:

A) Inverse exists
B) No inverse
C) Constant output
D) None

Answer: A
Explanation: Only bijections are invertible.

11. Vertical line test checks:

A) Relation
B) Function validity
C) Domain
D) Range

Answer: B
Explanation: Each x must have one y.

12. Horizontal line test checks:

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

Answer: B
Explanation: Determines injectivity.

13. f(x)=5 is:

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

Answer: B
Explanation: Same output for all inputs.

14. If function is both one‑one and onto:

A) Inverse impossible
B) Inverse exists
C) Constant
D) None

Answer: B
Explanation: Bijective ⇒ invertible.

15. Many‑one function example:

A) f(x)=x
B) f(x)=x²
C) f(x)=x³
D) f(x)=x+1

Answer: B
Explanation: Two inputs give same output.

16. One‑one function example:

A) x²
B) |x|
C) x³
D) Constant

Answer: C
Explanation: Strictly increasing.

17. Onto function example in R:

A) x²
B) x³
C) |x|
D) Constant

Answer: B
Explanation: Covers all real outputs.

18. If inverse exists, function must be:

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

Answer: B
Explanation: One‑one & onto required.

19. Domain of constant function is:

A) Single value
B) Entire set A
C) Empty
D) None

Answer: B
Explanation: Defined for all inputs.

20. Range of constant function has:

A) One element
B) Many elements
C) Infinite
D) None

Answer: A
Explanation: Output same always.

Objective Questions on Types of Functions Class 11 Mathematics

Objective Questions on Types of Functions Class 11 Mathematics

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