1. 1. Properties of Relations 2. 2. Set Theory: Subsets, Operations, and Counting 3. 3. Venn Diagrams and Real-World Set Applications 4. 4. Mathematical Sets: Solutions to Equations and Number Properties

1. 1. Relations (Types, Properties, and Set Logic) 2. 2. Domain of Functions 3. 3. Range, Extrema, and Global Properties 4. 4. Classification and Counting of Functions 5. 5. Functional Equations and Summation Series 6. 6. Composite Functions 7. 7. Inverse of a Function 8. 8. Greatest Integer [x] and Fractional Part {x} Functions 9. 9. Graphical Properties and Symmetry

1. 1. Fundamental Vieta’s Formulas and Basic Symmetric Functions 2. 2. Newton’s Identities and Recurrence Relations 3. 3. Complex Roots, Roots of Unity, and Trigonometric Roots 4. 4. Nature and Location of Roots 5. 5. Equations Reducible to Quadraticy & probability

1. 1. Nature of Roots (Real, Equal, Integral, and Signs) 2. 2. Expressions and Identities Involving Roots 3. 3. Equations with Absolute Values and Substitutions 4. 4. Exponential, Trigonometric, and Polynomial Functions 5. 5. Sets, Complex Numbers, and General Inequalities

1. 1. General Term, Properties of Terms, and Arithmetic Means 2. 2. Sum of A.P. and Series Summation 3. 3. Geometric Progression (G.P.) 4. 4. Arithmetico-Geometric Progressions (A.G.P.) and Infinite Series 5. 5. Special Series: Sum of Squares, Cubes, and Difference Methods 6. 6. Telescopic Series, Partial Fractions, and Rationalization 7. 7. Means (A.M., G.M., H.M.) and Harmonic Progressions (H.P.) 8. 8. Hybrid Progressions (A.P., G.P., and H.P. Combinations) 9. 9. Transcendental and Binomial-Based Series 10. 10. Recurrence Relations and Function-based Sequences 11. 11. Set Theory, Common Terms, and Number Properties

1. 1. Determinants and Adjoints 2. 2. Systems of Linear Equations 3. 3. Matrix Powers and Polynomials 4. 4. Special Matrices and Definitions 5. 5. Combinatorics, Counting, and Probability 6. 6. Matrix Algebra and Basic Operations & Matrix Inverses

1. 1. Non-Homogeneous Systems ($AX = B, B \neq 0$) 2. 2. Homogeneous Systems ($AX = 0$) and Non-Trivial Solutions 3. 3. Matrix Algebra, Inverse, and Adjoint Properties 4. 4. Evaluation, Range, and Properties of Determinants 5. 5. Area of Triangles and Coordinate Geometry & Progressions (A.P./G.P.) and Complex Numbers

1. 1. Trigonometric Identities and Algebraic Evaluations 2. 2. Trigonometric Equations and Roots 3. 3. Trigonometric Series and Products 4. 4. Function Ranges, Maximum and Minimum Values 5. 5. Inverse Trigonometric Functions and Related Series 6. 6. Inequalities, Properties, and Periodic Functions 7. 7. Practical Applications (Heights and Distances)

1. 1. Solving Inverse Trigonometric Equations and Determining Number of Solutions 2. 2. Simplification and Trigonometric Identities 3. 3. Domain and Range of Inverse Functions & Principal Values 4. 4. Series Summation & Maximum/Minimum Values & Calculus, Progressions,

1. 1. Centers and Properties of Triangles 2. 2. Locus of a Moving Point 3. 3. Point and Line Transformations 4. 4. Area and Coordinate Geometry Basics 5. 5. Equations of Lines and Concurrency 6. 6. Pair of Straight Lines 7. 7. Angles and Trigonometric Applications & Specialized

1. 1. Tangents and Normals 2. 2. Chord Properties and Midpoints 3. 3. Intersection of Circles 4. 4. General Equations and Geometric Properties 5. 5. Analytical Locus and Complex Plane Representation

1. 1. Individual Tangent/Normal Equations and Geometric Properties 2. 2. Common Tangents, Closest Points, and Inter-Curve Relationships 3. 3. Focal Chords and Focus 4. 4. Area Related Problems 5. 5. Vertex, Directrix, and Locus

1. 1.Standard Parameters and Eccentricity 2. 2.Tangents and Normals 3. 3.Chords and Intersection 4. 4.Area Problems

1. 1.Standard Equation and Parameters 2. 2.Eccentricity and Foci 3. 3.Tangents and Normals

1. 1. Standard Algebraic Limits & Rationalization 2. 2. Trigonometric & Inverse Trigonometric Limits 3. 3. L'Hopital's Rule & Series Expansion 4. 4. Infinite Limits, $1^\infty$ Forms & Series Summation 5. 5. Limits involving GIF $[x]$, Fractional Part $\{x\}$, and Continuity 6. 6. Methods of Differentiation 7. 7. Higher-Order Derivatives & Advanced Calculus Applications

1. 1. Limits and Indeterminate Forms 2. 2. Continuity of Functions 3. 3. Differentiability and Points of Non-Differentiability 4. 4. Differentiation Techniques and Functional Equations 5. 5. Mean Value Theorems (Rolle's and LMVT)

1. 1. Rate of Change of Quantities 2. 2. Tangents and Normals 3. 3. Monotonicity (Increasing and Decreasing Functions) 4. 4. Maxima and Minima (Local and Absolute) 5. 5. Mean Value Theorems & Geometric Appli 6. 6. Roots & Shortest Distance and Locus & Misc and Gen Analy

1. 1. Substitution, Algebraic Identities, and Trigonometric Simplification Part-1 2. 1. Substitution, Algebraic Identities, and Trigonometric Simplification Part-2 3. 2. Integration by Parts and Special Functional Forms 4. 3. Advanced Definite Integral Properties (King Rule, Symmetry, Periodic Functions) 5. 4. Integrals of Special Functions (GIF, Modulus, Fractional Part) 6. 6. Newton-Leibniz Rule, Functional Equations, and Differentiation 7. 5. Limit of a Sum

1. 1. Area Involving Circles and Conic Sections & Parabolas 2. 2. Area Bounded by a Parabola and Straight Lines 3. 3. Area Involving Absolute Value (Modulus) and Ine, qua. 4. 4. Area Bounded by (Trig Fun,Tangents,Exponential Log Fun.) 5. 5. General Functions, Piecewise Curves, and Integral Properties

1. 1. Linear Differential Equations (First Order) & Bernoulli's Form Part-1 2. 1. Linear Differential Equations (First Order) & Bernoulli's Form Part-2 3. 2. Variable Separable Method 4. 3. Homogeneous Differential Equations 5. 4. Formation, Order, and Degree of Differential Equations 6. 5. Integral Equations & Functional Equations 7. 6. Practical Applications (Growth, Decay, & Geometry)& Vector Components & Miscellaneous

1. 1. Scalar Product (Dot Product), Magnitudes, and Angles 2. 2. Vector Product (Cross Product) 3. 3. Scalar and Vector Triple Products 4. 4. Vector Projections 5. 5. Coplanarity and Collinearity 6. 6. Measurements: Areas and Volumes 7. 7. Vector Geometry (Points, Triangles, and Polygons) 8. 8. Vector Equations and Component Resolution&Rotation and Direction Cosines 9. 9. Mechanics (Statics and Dynamics)

1. 1. 3D Lines: Intersection, Direction Ratios, and Parallelism 2. 2. Shortest Distance Between Lines 3. 3. Point Mechanics: Foot of Perpendicular, Mirror Image, and Distance 4. 4. Planes: Equations, Intersections, and Families Part-1 5. 4. Planes: Equations, Intersections, and Families Part-2 6. 5. Angles and inclinations 7. 6. Geometric Shapes: Triangles, Tetrahedrons, and Spheres

1. 1. Modulus, Argument, and Polar Form Calculations 2. 2. Algebraic Identities, Conjugates, and Real/Imaginary Conditions 3. 3. Circles, Modulus Equations, and Metric Properties 4. 4. Linear Loci, Arguments, and Geometric Transformations 5. 5. Regions, Intersections (Sets), and Polygons 6. 6.Roots of Unity

1. 1. Linear Arrangements & Word Permutations 2. 2. Multiples, Divisibility, and GCD Constraints 3. 3. Digit Properties (Sums/Products) and Magnitude/Positional Constraints 4. 4. Combinatorial Selections (Teams & Committees) 5. 5. Dictionary Order (Rank) Problems 6. 6. Distribution Problems (Identical & Distinct Objects) 7. 7. Geometric Concepts 8. 8. Circular Permutations 9. 9. Combinatorial Identities & FormulaBased Problems 10. 10. Sets, Functions & Number Theory Concepts

1. 1. Term Independent of $x$ (Constant Term) 2. 2. Finding Coefficients of Specific Powers 3. 3. Ratios, Middle Terms, and Variable Determination 4. 4. Summation of Series and Calculus Applications 5. 5. Progressions, Ratios, and Equality Relations 6. 6. Rational, Irrational, and Integral Terms 7. 7. Remainders, Divisibility, and Number Theory 8. 8. Multinomial and Polynomial Expansions & Binomial Theorem 9. 9. Greatest Terms, Maximum Values, and Inequalities

1. 1. Arithmetic Mean and Basic Averages 2. 2. Mode and Median and Range 3. 3. Mean Deviation (MD) 4. 4. Variance and Standard Deviation (SD)& Arithmetic Progressions (A.P.) 5. 5. Combined Mean and Combined Variance/SD 6. 6. Correction and Adjustment of Statistical Data 7. 7. Effects of Change of Origin and Scale 8. 8. Probability Distributions and Random Variables & Theoretical Properties and Comparison

1. 1. Classical and Combinatorial Probability 2. 2. Conditional Probability 3. 3. Bayes' Theorem and Total Probability 4. 4. Binomial Distribution and Bernoulli Trials 5. 5. Independent Events and Set Operations 6. 6. Expectation, Variance, and Probability Distributions