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Relations And Functions — Revision Notes

AIIMS Paramedical · Mathematics

Quick revision notes for Relations And Functions — key concepts, formulas, and definitions for AIIMS Paramedical Mathematics preparation.

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Revision Notes — Relations And Functions

Key concepts, formulas, and definitions from Relations And Functions for AIIMS Paramedical Mathematics preparation.

Key Topics to Revise

1

Cartesian Product of Sets

  • Cartesian product X × Y is the set of all ordered pairs (x,y) where x ∈ X and y ∈ Y
  • If n(X) = p and n(Y) = q, then n(X × Y) = pq
  • Order matters in Cartesian products: X × Y ≠ Y × X (unless X = Y)
2

Relations

  • A relation R from X to Y is any subset of X × Y
  • Domain of R = set of all first elements in ordered pairs of R
  • Range of R = set of all second elements in ordered pairs of R
3

Functions

  • A function f: X → Y is a special relation where each element in X maps to exactly one element in Y
  • For functions: Domain = X, Co-domain = Y, Range ⊆ Y
  • Vertical Line Test: A graph represents a function if every vertical line intersects it at most once
4

Types of Functions

  • Identity Function: f(x) = x for all x in domain
  • Constant Function: f(x) = c for all x in domain
  • Polynomial Function: f(x) = a₀ + a₁x + a₂x² + ... + aₙxⁿ

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Key Concepts

For nonA relation R from set XA function fIdentity FunctionFor functions f

Frequently Asked Questions

What topics are covered in Relations And Functions for AIIMS Paramedical?
Relations And Functions is an important chapter in AIIMS Paramedical Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Cartesian Product of Sets, Relations, Functions, Types of Functions.
How important is Relations And Functions for AIIMS Paramedical?
Relations And Functions is a frequently tested chapter in AIIMS Paramedical Mathematics. Questions from this chapter appear regularly in previous year papers. There are 174 practice questions available for this chapter.
How to prepare Relations And Functions for AIIMS Paramedical?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.

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