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### Algebra

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** Set theory**

- Introduction to set
- Subset and power set
- Intersectoin of sets
- Union of sets
- Difference of sets
- Complement of sets
- Properties of Operations on Sets
- Intervals
- Cardinal number of set

**Intervals Inequalities**

- Linear inequalities in one variable
- Linear inequalities in two variables
- Values of square
- Values of reciprocal
- Sign Scheme Method

** Modulus of real number**

- Modulus_Introduction
- General definition of modulus and equations
- Inequalities involving Modulus
- Modulus Advanced

** Relation and functions **

- Relation and Functions

** Complex Numbers**

- Introduction to imaginary number
- Structure of complex number and its operations
- Comparison of complex numbers
- Polar form of complex number
- Properties of polar form
- De-Moivres theorem
- Cube roots of unity
- Collinearity of origin and two non-zero complex numbers
- Inequalities
- Locus based on modulus_Theory
- Locus based on Modulus of Complex Number Questions
- Angle between two lines
- Geometry using Argument of complex numbers
- Rotation formula in complex numbers

** Quadratic Equations**

- General
- Remainder and factor theorem new
- Nature of roots
- Sum and product of roots
- Common roots
- Use of discriminant
- Sign of quadratic function
- Location of roots

**Logarithm**

- Exponential Function
- Logarithm and logarithmic function
- Properties of logarithm_Part I
- Properties of logarithm_Part II
- Logarithmic equations
- Logarithmic inequalities

** Progression and Series**

- General term of AP
- Sum of AP
- GP and its general term
- Sum of n terms of GP
- Harmonic Progression
- Sigma operator and method of difference
- Finding nth term from the given sum of n terms
- Multiple sigma with dependent & independent variables
- AGP
- Sum of series by method of difference_I
- Sum of series by method of difference_II

** Binomial Theorem**

- Binomial expansion – general
- Finding coefficients
- Sum of coefficients
- Greatest term
- Series – part 1
- Series – part 2
- Miscellaneous

** Permutation and Combination**

- Factorial notations
- Counting principal
- Permutations of distinct objects
- Permutation of objects in which some objects are identical
- Circular permutations
- Combination – formula
- Problems based on combinations
- Problems based on combinations – part 2
- All possible selections
- Division distribution of distinct objects
- Distribution of identical objects
- Principle of inclusion and exclusion
- Derangement

### Trigonometry

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** Trigonometric ratios and identities **

- Measurement of angle and trigonometry function for more than right angle
- Graphs of trigo. functions and their range
- Trigonometric ratios for allied angles
- Problems based on trig. identities
- Trig. Ratios for Compound angles
- C- D formula
- Multiple angle formulas_Part I
- Multiple angle formula_Part II
- Important results of multiple angle formula
- Multiple angle formula_Part III
- Value of sin 18 and cos 36
- Range of expression using trig. substitution
- Trigonometric inequalities in triangle

** Trigonometric equations**

- Trigonometric Equations – Part 1
- Trigonometric Equations – Part 2
- Important points for solving trigonometric equations
- Trigonometric Equations based on extreme values

** Properties and Solution of triangles**

- Sine rule
- Cosine rule
- Projection rule, half angle formula, area of triangle
- Circumcentre, incentre and lengths associated with it
- Orthocentre and lengths associated with it
- Ex-centers and lengths associated with it

### Coordinate Geometry

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**Cartesian coordinate system and Straight Lines **

- Section formula
- Area of triangle
- Slope of line
- Centroid of triangle
- Incenter of triangle
- Orthocentre of triangle
- Equation of line – Point slope form
- Equation of line – slope intercept form
- Equation of line – intercept form
- Parametric form of straight lines_1
- Parametric form of straight lines_2
- Family of st. lines
- Distance of point from the line
- Equation of angle bisectors
- Concurrency of lines
- Position of point w.r.t. line
- Locus
- Pair of straight lines_introduction
- Angle between pair of straight lines
- Homogenization

**Circles**

- Circle equation
- Circle equation – part 2
- Tangent to circle
- Radical axis and different cases of two circels
- Angle between circles and orthogonal intersection
- Family of circles
- Locus problem

** Parabola**

- Equation of parabola
- Focal Chord
- Tangent having given slope_Tangent at a given point on the curve_Theory
- Tangent having given slope_Tangent at a given point on the curve_Problems discussion
- Common Tangent
- Tangent from external point
- Properties of Tangent of parabola
- Normal to parabola at a point on it or having given slope
- Normal to parabola from a point not lying on it
- Normal – chord of contact to parabola

** Ellipse**

- Equation of ellipse
- Tangent to ellipse_Theory
- Tangent to ellipse at at point on it_Problems discussion
- Tangent having given slope and tanent from outside point
- Director Circle of Ellipse
- Tangent and normal to ellipse

** Hyperbola**

- Hyperbola – equation
- Hyperbola – tangent – normal – coc etc
- Reflection property of ellipse and hyperbola

### Algebra/Vectors & 3D Geometry

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**Determinant **

- Introduction and Expansion of Determinant
- Sarrus rule of expansion
- Properties of determinant_Theory
- Problems based on property of determinant_NCERT Based
- Problems based on properties of determinant_Part II
- Problems based on properties of determinant_Part III
- Differentiation of Determinant
- Product of determinants
- System of equations in two variables
- System of equations in three variables

**Matrices**

- Elementary matrices
- Product of matrices, transpose of matrices
- Adjoint and inverse of matrices
- Special matrices and system of equations
- Problems based on determinant of matrix

**Probability**

- Probability – elementary
- Independent events
- Dependent events and total probability theorem
- Bayes theorem

**Introduction to Vectors**

- Vectors(introduction)
- Dependent and independent vectors
- Dot and cross product
- Vector triple product
- Finding Vector
- Finding Vector by Solving Vector Equations
- Vector_Tetrahedron

**3-D Geometry **

- Straight lines
- Plane – part 1
- Plane – part 2
- Line and plane in space
- Line and plane in space

### Calculus/ITF

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**Inverse Trigonometric Functions(ITF)**

- Domain, range, graphs of trigonometric inverse functions
- Principal Values of Inverse of sine_more detailed
- Principal values of cos inverse function_More detailed
- Relating Different ITF
- Simplifying ITF using substitution
- Complementary angles
- Sum of two arctanRX
- Addition-subtration of two or more inverse trigonometric functions
- Addition and subtration of angles in terms of cos inverse function

**Functions and Relations **

- Inequalities and its use in functions
- Modulus function
- Sign scheme method for solivng inequalities
- Domain and Range of Functions involving trigonomteric functions
- Domain and range of functions involving itf_video
- Exponential & Logarithmic functions
- Greatest integer, fractional part, signum and other miscellaneous functions
- Odd and even functions
- One-one, many-one, onto and into functions
- Periodic functions
- Functional Equations_part_1
- Functional Equations_Part_2
- Functional Equations_Part_3
- Functional Equations_Part 4
- Identical functions
- Graphical transformations
- Inverse functions
- Injectivity & Surjectivity of composite functions

**Limits **

- Limits – elementary
- Limits – algebraic
- Limits – trigonometric
- Limits – exp and logarithm
- Limits – One power infinity form_Part I
- One power infinity_Shortcut formula
- Limits – L’Hopital rule
- Limits – use of expansion
- Limits – finding unknowns

**Continuity of Function **

- Continuity – definition
- Continuity of functions involving GIF_Part 1
- Continuity of functions involving GIF_Part II
- Cont. of fun. differently defined for rational and irrational numbers
- Algebraic operations of cont.-disc. functions
- Application of cont. functions and intermediate value theorem
- Differentiability of product function_Important concept

**Differentiability of Functions **

- Differentiability – part 1
- Differentiability – part 2

**Method of Differentiation**

- Differentiation – elementary
- Differentiation using chain rule
- Differentiation involving inverse trigo. functions
- Differentiation of implicit functions
- Differentiation using Logarithm
- Differentiation of functions in parametric form
- Differentiation of determinant and misc.
- Successive differentiation
- Finding function or derivative from functional equation
- Differentiation of inverse function

**Application of Derivatives**

- Tangent and normals
- Angle between curves
- Application of Tangent – normal
- Approximations
- Rolle’s Theorem
- Rolle’s theorem_Selecting function
- LMVT

**Monotonocity and Extremum of Functions **

- Monotonocity
- Finding number of roots using monotonicity
- Inequalities using monotonicity
- Maxima-minima of functions
- Maxima_Minima when critical points cannot be evaluated
- Applications of maxima-minima
- Graph plotting_1
- Graph plotting_2

**Indefinite Integration**

- Indefinite integration(elementary)
- Integration by elemnetary substitution
- Reciprocal of quadratic
- Integration by partial fractions
- Integration by parts
- Integration by typical substitution
- Integration of irrational function_substitution technique

** Definite Integration **

- Definition and definite integration as limit of sum
- Properties of definite integration_Part I
- Properties of definite integration_Part II
- Properties of definite integration_Part III
- Definite integration of odd – even and periodic functions
- Substitution and by parts
- Reciprocal Substitution Definite Integration
- Substitution techniques in definite integration
- Leibnitz forumla and inequalities
- Miscellaneous

** Area **

- Area bounded by curve and axis
- Area bounded by two curves
- Area bounded by curves involving Trigonometric Function
- Area bounded by curves involving logarithmic function
- Area bounded by implicit functions
- Finding Area without integration

** Differential Equation**

- Differential equations (elementary)
- Forming Differential Equations
- Solving Differential equations by variable sepration
- Solving Homogeneous differential equations
- Solving Linear Differential Equations
- Solving Equations reducible to L.D.E.
- Solving Differential equation by general form of variable seperation
- Application of Differential equation – Geometrical
- Application of Differential equation – Physics problems