One-to-One & Onto Functions MCQs with Solutions
One‑to‑One & Onto Functions MCQs with Solutions
Class: CBSE Class 12 Mathematics
Subject: Mathematics
Section: Relations and Functions
Topic: One‑to‑One & Onto Functions
Board: CBSE Board Examinations
Subject: Mathematics
Section: Relations and Functions
Topic: One‑to‑One & Onto Functions
Board: 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 Examination standard practice.
Q1. A function is one‑to‑one if:
Answer: B
Explanation: Injective functions assign unique images to unique elements.
Explanation: Injective functions assign unique images to unique elements.
Q2. Onto function means:
Answer: B
Explanation: Every codomain element must have a pre‑image.
Explanation: Every codomain element must have a pre‑image.
Q3. One‑one & onto together form:
Answer: B
Explanation: Bijective = Injective + Surjective.
Explanation: Bijective = Injective + Surjective.
Q4. f(x)=x³ on R is:
Answer: C
Explanation: Strictly increasing and covers all real values.
Explanation: Strictly increasing and covers all real values.
Q5. f(x)=x² on R is:
Answer: C
Explanation: f(2)=f(‑2); negatives not in range.
Explanation: f(2)=f(‑2); negatives not in range.
Q6. Inverse exists only for:
Answer: C
Explanation: Must satisfy both properties.
Explanation: Must satisfy both properties.
Q7. f:N→N, f(x)=x+1 is:
Answer: B
Explanation: 1 has no pre‑image.
Explanation: 1 has no pre‑image.
Q8. f(x)=2x+3 on R is:
Answer: A
Explanation: Linear function with non‑zero slope → bijection.
Explanation: Linear function with non‑zero slope → bijection.
Q9. Constant function is:
Answer: C
Explanation: All inputs map to same output.
Explanation: All inputs map to same output.
Q10. Identity function is:
Answer: A
Explanation: Perfect one‑one & onto mapping.
Explanation: Perfect one‑one & onto mapping.
Q11. Range of onto function equals:
Answer: B
Explanation: Surjection definition.
Explanation: Surjection definition.
Q12. Many‑one onto is:
Answer: A
Explanation: Coverage possible despite repetition.
Explanation: Coverage possible despite repetition.
Q13. Injective test:
Answer: A
Explanation: Standard injectivity condition.
Explanation: Standard injectivity condition.
Q14. f(x)=e^x on R is:
Answer: A
Explanation: Range (0,∞).
Explanation: Range (0,∞).
Q15. f(x)=ln x is onto:
Answer: B
Explanation: Log covers all real outputs.
Explanation: Log covers all real outputs.
Q16. Quadratic functions are generally:
Answer: B
Explanation: Symmetry about vertex.
Explanation: Symmetry about vertex.
Q17. Linear function slope ≠0 is:
Answer: A
Explanation: Strict monotonicity ensures bijection.
Explanation: Strict monotonicity ensures bijection.
Q18. Inverse of bijection is:
Answer: A
Explanation: Unique mapping preserved.
Explanation: Unique mapping preserved.
Q19. Onto mapping ensures:
Answer: A
Explanation: Entire codomain mapped.
Explanation: Entire codomain mapped.
Q20. Bijective ⇒ inverse is:
Answer: A
Explanation: One‑to‑one correspondence guarantees uniqueness.
Explanation: One‑to‑one correspondence guarantees uniqueness.