Chapter 2 · Class XI · NCERT Exercises

Relations & Functions — Exercises

Every Domain, Every Range — Complete NCERT Relation & Function Solutions

📂 4 Exercises📝 36 Questions
▶ Start Exercise 2.1📖 Notes

Exercise Index

①

Exercise 2.1

Cartesian product A×B; ordered pairs; n(A×B)

10 QEasy
→
②

Exercise 2.2

Relations; domain, co-domain & range

9 QModerate
→
③

Exercise 2.3

Functions; algebra of functions; domain of f±g

5 QModerate
→
★

Miscellaneous

Graphs: modulus, GIF, signum; composite domain

12 QHard
→

4 files · 36 questions

Chapter Snapshot

JEE MainCBSE BoardsNEET
10Concepts
8Formulas
ModerateDifficulty
5–7%Weightage

Before You Begin

Prerequisites

  • ✓Ch 1 — Sets
  • ✓Coordinate geometry basics
  • ✓Function intuition (Class X)

Have Ready

  • 🔧Graph paper
  • 🔧NCERT textbook
  • 🔧Ruler

Exercise Topic Map

Exercise 2.1List A×B as ordered pairs; verify n(A×B)=n(A)·n(B)
Exercise 2.2Relation as subset of A×B; extract domain and range
Exercise 2.3Function verification; evaluate f(x); compute (f+g)(x)
MiscellaneousSketch |x|, sgn(x), ⌊x⌋; domain of composite functions

Key Formulae

\(n(A \times B) = n(A) \cdot n(B)\)
\((f+g)(x) = f(x) + g(x)\)
\(\text{Domain of } \sqrt{f(x)}: f(x) \geq 0\)
\((f \circ g)(x) = f(g(x))\)

NCERT Solving Method

Step 1 — Cartesian product: list all (a,b) pairs systematically. Step 2 — Relations: extract domain (first elements) and range (second elements). Step 3 — Functions: every domain element must have exactly ONE image. Step 4 — Combined domain: find each restriction independently then intersect.

Continue Your Preparation

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