Types of Relations: Empty, Reflexive, Symmetric, Transitive

Understand different types of relations with examples and properties.

Types of Functions: One-One, Onto, Bijective

Learn classification of functions with graphical representations.

Inverse of a Function and Binary Operations

Master the concept of inverse functions and binary operations.

Domain, Range and Graphs of Inverse Trig Functions

Learn restrictions and graphical behavior of inverse trig functions.

HOTS and Important Questions on Inverse Tirgonometry Functions

Properties and Elementary Results

Understand key properties and formulas for inverse trigonometric functions.

Types of Matrices: Symmetric, Skew-Symmetric, Orthogonal

Classify matrices based on their properties and characteristics.

Matrix Operations: Addition, Multiplication, Transpose

Perform algebraic operations on matrices with examples.

Inverse of Matrix using Adjoint and Determinants

Learn to find inverse of square matrices using adjoint method.

Properties of Determinants

Understand important properties to simplify determinant calculations.

Area of Triangle using Determinants

Apply determinants to find area of triangles given vertices.

Solution of Linear Equations using Cramer’s Rule

Solve system of linear equations using determinant methods.

Continuity of Functions

Check continuity of functions at points and in intervals.

Differentiability and Derivatives

Understand relationship between continuity and differentiability.

Chain Rule, Implicit and Logarithmic Differentiation

Master advanced differentiation techniques.

Rate of Change and Tangents/Normals

Apply derivatives to solve real-world rate problems.

Increasing/Decreasing Functions

Use derivatives to analyze function behavior.

Maxima and Minima (Optimization Problems)

Solve applied problems using calculus concepts.

Integration Methods: Substitution, Partial Fractions, By Parts

Learn various techniques to find indefinite integrals.

Learn how to tackle various types of Integrals problems .

Definite Integrals and Properties

Evaluate definite integrals using fundamental theorem.

Area Under Curves

Calculate area bounded by curves using integration.

Order and Degree of Differential Equations

Classify differential equations based on order and degree.

Solution Methods: Variable Separable, Homogeneous, Linear

Solve first order differential equations using different methods.

Dot and Cross Product of Vectors

Understand vector multiplication operations.

Scalar and Vector Triple Product

Learn advanced vector product concepts.

Direction Cosines and Ratios

Understand orientation of lines in 3D space.

Equation of Line and Plane

Learn different forms of line and plane equations.

Angle Between Lines and Planes

Calculate angles between geometric elements in 3D.

Graphical Method for Optimization

Solve linear programming problems graphically.

Feasible and Optimal Solutions

Identify feasible regions and optimal points.

Conditional Probability and Multiplication Theorem

Understand dependent events and probability rules.

Bayes’ Theorem and Applications

Solve probability problems using Bayes’ rule.

Random Variables and Probability Distributions

Learn about discrete random variables and their distributions.