Relations and Functions in past papers.

CBSE Board Examination 2026

• Board 2026 Q32$|x - y|$ divisible by a prime $p$ as an equivalence relation, or $f(x) = \frac{3x + 2}{5x - 3}$ one-one and onto
  Equivalence relation; one-one and onto function5 marks

CBSE Board Examination 2025

• Board 2025 Q19Is $f(x) = 3x - 5$ a bijection from Z to Z?
  Bijective functions1 mark
• Board 2025 Q37Case study: five relations on $\{1, 2, 3\}$
  Case study: reflexive, symmetric, transitive4 marks

CBSE Board Examination 2024

• Board 2024 Q1Is $f(x) = 4x + 3$ on $R_+$ one-one or onto?
  One-one and onto functions1 mark
• Board 2024 Q26Is $|x^2 - y^2| < 8$ on $\{1, \ldots, 5\}$ reflexive, symmetric, transitive? or $f(x) = ax + b$ one-one and onto
  Relation properties; one-one and onto function3 marks

CBSE Board Examination 2023

• Board 2023 Q21The set B for a one-one onto $f(x) = 2x$⁠, or $\sin^{-1}\left(\sin\frac{3\pi}{4}\right) + \cos^{-1}\left(\cos\frac{3\pi}{4}\right) + \tan^{-1}1$
  One-one onto function; inverse trig values2 marks
• Board 2023 Q32Is $R = \{(x, y) : x\cdot y$ is irrational$\}$ reflexive, symmetric, transitive?
  Reflexive, symmetric, transitive: x·y irrational5 marks

CBSE Sample Paper 2026-27

• Sample 2026-27 Q32Is $(a, b)R(c, d) \Leftrightarrow a^2 + d^2 = b^2 + c^2$ an equivalence relation; or is $y = x^2 + 5$ injective, surjective
  Equivalence relation; injective and surjective5 marks

CBSE Sample Paper 2025-26

• Sample 2025-26 Q36Case study: one-way traffic flow between five spots as a relation
  Relations: reflexive, transitive, function4 marks

CBSE Sample Paper 2024-25

• Sample 2024-25 Q20Is $f(x) = \sec x$ one-one on its domain?
  One-one functions: sec x and the line test1 mark
• Sample 2024-25 Q37Case study: relations and functions on the finalists of a bike race
  Relations: counting, equivalence; one-one and onto4 marks

CBSE Sample Paper 2023-24

• Sample 2023-24 Q20Is $\{(1, x), (2, y), (3, z)\}$ a bijection from $\{1, 2, 3, 4\}$⁠?
  One-one, onto and bijective functions1 mark
• Sample 2023-24 Q33$(a, b)R(c, d) \Leftrightarrow ad = bc$ on $\mathbb{N} \times \mathbb{N}$⁠, or $f(x) = \frac{x}{1 + |x|}$ is one-one and onto
  Equivalence relation and class; one-one and onto5 marks

CBSE Sample Paper 2022-23

• Sample 2022-23 Q33$(a, b)\,R\,(c, d) \iff ad = bc$ is an equivalence relation, or $A \subset B$ on $P(X)$
  Equivalence relation; reflexive, transitive only5 marks

CBSE Sample Paper 2020-21

• Sample 2020-21 Q1Is $f(x) = x^3$ one-one? Or: the number of reflexive relations on a 3-element set
  One-one functions; counting reflexive relations1 mark
• Sample 2020-21 Q2Which pair to remove from $R$ to make it an equivalence relation
  Equivalence relations1 mark
• Sample 2020-21 Q3Is $\{(a, b) : \sqrt a = b\}$ a function? Or: union and intersection of equivalence classes
  Functions as relations; equivalence classes1 mark
• Sample 2020-21 Q29$a + b$ divisible by 2 on $Z$⁠: reflexive, symmetric, transitive, and $[0]$
  Equivalence relation and an equivalence class3 marks

Questions that also use Relations and Functions

Their main topic is in another chapter.

• Board 2024 Q38Case study: the inverse of the sine function
  Inverse sine: branches, value, graph, domain4 marks
• Sample 2022-23 Q21$\sin^{-1}\left[\sin\frac{13\pi}{7}\right]$⁠, or an onto function on $N$ that is not one-one
  Principal value of sin⁻¹; onto, one-one functions2 marks