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Relations and Functions — Study Plan

Madhya Pradesh Board · Class 12 · Mathematics

A step-by-step study plan for Relations and Functions, Madhya Pradesh Board Class 12 Mathematics: what to learn first, what to practise and when to revise.

119 questions52 flashcards15 formulas & key relations5 concepts

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A visual representation of the Cartesian product A × B using a grid or mapping diagram, showing how ordered pairs are formed.
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Study Plan

1
Day 1–2

Learn the Theory

Read the textbook chapter carefully. Note down definitions, formulas and key ideas. Focus on: 1. Relations and Their Types, 2. Functions: One-One, Onto, and Bijective, 3. Composition of Functions and Inverse.

2
Day 3

Practise

Solve the textbook exercises and extra practice questions. There are 119 questions available for this chapter.

3
Day 4

Revise & Test

Revise key points without looking at your notes. Take a practice quiz and mark weak areas for another pass.

4
Day 7

Spaced Revision

Come back to Relations and Functions after a week. Use flashcards for quick recall and try past exam questions on this chapter.

What to Focus On

  • A relation in A is a subset of A × A.
  • Empty relation: R = ϕ.
  • Universal relation: R = A × A.
  • Equivalence classes are mutually disjoint.
  • The union of all equivalence classes is the whole set.
  • For 2 divides a-b on Z, [0] is the even integers and [1] is the odd integers.
  • One-one means distinct inputs have distinct outputs.
  • Many-one means different inputs may have the same output.
  • Onto means every codomain element has a preimage.

Common Mistakes to Avoid

A relation from a set to itself must connect every element to every other element.

Empty relation and universal relation mean the same thing.

If a relation is symmetric, then it must also be transitive.

Memory Tips

Empty relation and universal relation

Reflexive, symmetric, transitive

Equivalence relation as partition

Relation on integers given by 2 divides a-b

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Frequently Asked Questions

What are the important topics in Relations and Functions for Madhya Pradesh Board Class 12 Mathematics?
Key topics in Relations and Functions include Relations and Their Types, Functions: One-One, Onto, and Bijective, Composition of Functions and Inverse, Historical Development of Function. Study these first, then practise questions on each for the Madhya Pradesh Board Class 12 board exam.
How should I revise Relations and Functions for the Madhya Pradesh Board Class 12 board exam?
Learn the core ideas first, then work through the 119 practice questions on Relations and Functions. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All Madhya Pradesh Board Class 12 Mathematics Study Plan

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