Chapter 20 · Class 11-12 & JEE Main/Adv
Number System & Basics
33 topics in 12 parts
Principle of Mathematical Induction (PMI) Mathematical Statements & Logical Connectives Truth Tables Tautology & Contradiction Conditional & Bi-Conditional Statements Quantifiers
Key ideas
Analytical Comparison & Distinction Matrix
| Analytical Method | Standard Representation | Parametric / Invariant Framework |
|---|---|---|
| Algebraic Nature | Explicit equations relating spatial coordinates | Parameterized using scalar parameters (λ, μ) or vectors |
| Symmetry Usage | Relies on coordinate expansion | Exploits vector dot/cross products for rapid simplification |
| Computational Efficiency | Direct for intercept evaluation | Superior for angles, orthogonal projections, and distances |
| Common Mistake | Sign confusion in determinants | Omitting boundary condition checks |
All 33 topics in Number System & Basics
Principle of Mathematical Induction
- Induction Proofs & Divisibility Statements
- Summation & Inequality Proofs by Induction
Types of Statements & Logical Connectives
- Simple & Compound Statements
- Conjunction, Disjunction & Negation
Truth Tables, Tautology & Contradiction
- Formation & Evaluation of Truth Tables
- Tautology & Contradiction Identification
- Logical Equivalence of Statements
Conditional & Bi-Conditional Statements
- Implication & Truth Table
- Converse, Inverse & Contrapositive
- Bi-conditional Statements
Validity of Statements & Quantifiers
- Universal & Existential Quantifiers
- Methods of Proof & Validity of Statements
- Set Theory Usage in Logic
Factorials & Prime Power Exponents
- Exponent of Prime in n! (Legendre's Formula)
- Unit & Ten's Digits of Factorials
- Factorial Simplification & Equations
GCD & LCM
- Properties & Relation of GCD & LCM
- Counting Integral Pairs with Given GCD/LCM
- Word Problems & Applications
Divisibility Rules & Divisor Properties
- Tests of Divisibility & Digit Conditions
- Number & Counting of Divisors
- Sum & Product of Divisors
Modular Arithmetic & Cyclicity
- Remainder Calculation & Modular Congruence
- Cyclicity & Last Digits of Powers
Surds & Radicals
- Square Root of Quadratic Surds
- Simplification & Rationalization of Surds
- Integer Part & Radical Inequalities
Algebraic Identities & Digit Problems
- Expansion & Value Evaluation of Algebraic Identities
- Digit-based Number Problems & Reversal
- Base & Number Representation
Diophantine Equations & Number Theory
- Integral Solutions of Equations
- Perfect Squares & Perfect Cubes Conditions
- Rational & Irrational Numbers Properties