CBSE Class 12 Mathematics 2026 Main Paper 65/5/1 · Q364 Marksrelations_and_functions
CBSE Class 12 Mathematics 2026 Main Paper 65/5/1 · Question 36 (Relations And Functions)
A sustainability project selects four girls A={G₁,G₂,G₃,G₄} and three boys B={B₁,B₂,B₃}.
Part (1) 1 Marks
How many relations from A to B are possible?
Answer: 4096.
- There are 4·3=12 pairs in A×B.
- Each subset is a relation, so there are 2¹²=4096.
Part (2) 1 Marks
Is R={(G₁,B₁),(G₂,B₂),(G₃,B₂),(G₄,B₃),(G₁,B₂)} an injective function?
Answer: No. R is not a function.
- G₁ is related to both B₁ and B₂.
- A function has exactly one image per input, so injectivity as a function does not apply.
Part (3) 2 Marks
On A, two students are related if they live in the same colony. Is this an equivalence relation?
Answer: Yes.
- A student lives in the same colony as themself, giving reflexivity.
- Sharing a colony is symmetric.
- If two successive pairs share a colony then all three live there, giving transitivity.
Part (4) 2 Marks
Can any function f:B→A be bijective?
Answer: No.
- B contains three elements and A contains four.
- The image of a function on B has at most three elements.
- Thus it cannot be onto A or bijective.