Monomath – CBSE | GSEB | IB | JEE Maths by Ajay Yadav (Math King of Katargam) – 15+ Years Experience. Study Notes, Video Lessons, Formula Sheets & PYQs.
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Relations and Functions

Previous Year Questions (2022-2024)

📅 Year 2022

  1. Check if f: R -> R defined by f(x) = 2x - 3 is bijective.
    Show Solution
    Injective: f(x1)=f(x2) => 2x1-3=2x2-3 => x1=x2\nSurjective: for any y, x=(y+3)/2 exists\nHence bijective.
  2. Let R = {(x,y): x,y ∈ Z, x-y is multiple of 5}. Show R is equivalence relation.
    Show Solution
    Reflexive: x-x=0 multiple of 5.\nSymmetric: if x-y=5k then y-x=-5k multiple of 5.\nTransitive: x-y=5k, y-z=5m => x-z=5(k+m) multiple of 5.\nHence equivalence relation.

📅 Year 2023

  1. Check if f: R -> R defined by f(x) = 2x - 3 is bijective.
    Show Solution
    Injective: f(x1)=f(x2) => 2x1-3=2x2-3 => x1=x2\nSurjective: for any y, x=(y+3)/2 exists\nHence bijective.
  2. Let R = {(x,y): x,y ∈ Z, x-y is multiple of 5}. Show R is equivalence relation.
    Show Solution
    Reflexive: x-x=0 multiple of 5.\nSymmetric: if x-y=5k then y-x=-5k multiple of 5.\nTransitive: x-y=5k, y-z=5m => x-z=5(k+m) multiple of 5.\nHence equivalence relation.

📅 Year 2024

  1. Check if f: R -> R defined by f(x) = 2x - 3 is bijective.
    Show Solution
    Injective: f(x1)=f(x2) => 2x1-3=2x2-3 => x1=x2\nSurjective: for any y, x=(y+3)/2 exists\nHence bijective.
  2. Let R = {(x,y): x,y ∈ Z, x-y is multiple of 5}. Show R is equivalence relation.
    Show Solution
    Reflexive: x-x=0 multiple of 5.\nSymmetric: if x-y=5k then y-x=-5k multiple of 5.\nTransitive: x-y=5k, y-z=5m => x-z=5(k+m) multiple of 5.\nHence equivalence relation.