Chapter 14 · Class 11-12 & JEE Main/Adv
Inequalities & Modulus
24 topics in 7 parts
Number System & Intervals Greatest Integer Function Fractional Part Function Open & Closed Intervals Standard Inequalities Generalized Method of Intervals
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 24 topics in Inequalities & Modulus
Constant & Variables
- Dependent & Independent Variables
- Number System & Basic Concepts
Function
- Definition of Functions
- Greatest Integer Function, Fractional Part Function
Intervals
- Closed Interval
- Open Interval
- Semi-open or Semi-closed Interval
Inequalities
- Frequently Used Inequalities
- Generalized Method of Intervals
- Important Facts
- System of Inequalities
- Integer Solutions
- Parametric Inequalities
Generalized Method of Intervals for Solving Inequalities
- Sign Scheme of f(x)=f₁(x)f₂(x)f₃(x).....fn(x)
- Solving Irrational Inequalities
- Polynomial & Rational Inequalities
- Trigonometric, Exponential & ITF Inequalities
Modulus Function
- Inequalities Involving Absolute Value
- Modulus Equations
- Modulus Inequalities
- Modulus Quadratic Equations
AM-GM & Cauchy-Schwarz Inequalities
- AM-GM Inequality
- Inequalities Involving Simple A.M., G.M., H.M.
- Cauchy-Schwarz Inequality & Constrained Optimization