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JEE Main BArch Syllabus- Mathematics
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Topic
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Sub-topics
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Sets, relations and functions
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Sets, roster and set builder form of sets, Types of sets, subset, the proper and improper sets, Power set, universal set, union of sets, complement of sets, De-morgan’s Law, Ordered pairs, cartesian product, Relation, number of relation, types of relation, Functions, image, and Pre-image, Types of functions, Composition of function, condition for composite function, the property of a composite function, The inverse of a function
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Complex numbers and quadratic equations
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Algebra of complex numbers, Modulus and argument of complex numbers, The complex conjugate of complex numbers and properties of complex numbers, Polar form representation and Euler form, Finding the square root of complex numbers and complex equations, De-moivre’s theorem, cube root and nth root of unity, Vector representation and rotation, The discriminant of quadratic equation, Nature of roots, the relation of coefficient and roots, Transformation of quadratic equations and condition of common roots.
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Matrices and Determinants
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Matrix and operation on matrices, Types of matrix, Transpose of a matrix, symmetric and skew-symmetric matrix, Conjugate of matrix, hermitian and skew-hermitian matrix, Determinant of matrix, Minor and cofactor of an element of matrix/determinant, Adjoint and inverse of a matrix, Elementary row operations and use in finding the inverse of a matrix, System of linear equations and Cramer’s Rule, System of homogeneous linear equations
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Permutations and Combinations
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Fundamental Principle of Counting, Permutations as an Arrangement, Combinations as Selections, P (n,r) and C (n,r), Application of Permutation and Combination.
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Mathematical Induction
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Principle of Mathematical Induction and its Simple Application, Principle of Mathematical Induction.
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Binomial Theorem and its simple applications
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Binomial Theorem for Positive Integral Index, Pascal’s Triangle, General Term, Middle Term, Properties and Application of Binomial Theorem.
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Sequence and Series
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Sequences, Arithmetic and Geometric Progression, Arithmetic and Geometric Mean, Harmonic Progression, Sum up to n terms, Arithmetic-geometric series.
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Limit, Continuity and differentiability
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Limits of a function, Properties of limits, Limits of polynomials and rational functions, Continuity of a function at a point, Discontinuity, Continuity of Composite Functions, Differentiability, Algebra of derivatives, Rolle’s Theorem, Mean Value Theorem (Lagrange).
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Integral Calculus
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Introduction, integration as the inverse function of differentiation, Indefinite integral and properties of indefinite integral, Comparison between definite and Indefinite integral, Methods of integration, Integration by substitution, Integration using trigonometric identities, integration by partial fractions, integration by parts, Integrals of some particular function, Integrals of some special types, Definite integral and its properties, The fundamental theorem of calculus, Evaluations of definite integral by substitution.
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Differential equations
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Order and Degree of a Differential equation, General and Particular solution, Formation of differential equations, Methods of solving different types of differential equations.
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Coordinate Geometry
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Directrix, Latus Rectum, Slope and gradient, Focus and Eccentricity, Angle between two intersecting lines, their intersection points, parallel lines and collinear lines are the important terms of Coordinate Geometry.
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Three dimensional Geometry
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Coordinate of a point in space, distance formula, Direction cosine and Direction ratio, The angle between two intersecting lines, Skew lines and the shortest distance between two lines, Equation of line and plane, The intersection of line and plane.
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Vector Algebra
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Vector (Position Vector, Direction cosine), Types of vector, Vector Algebra, Detection Formula, Product of two vectors (Scalar and Vector product).
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Statistics and Probability
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Independent Events, Dependent Events, Conditional probability, Random variables, etc.
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Trigonometry
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Trigonometry Function and their Identities, Trigonometry Equation, Inverse Trigonometry.
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Mathematical Reasoning
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Statements and types of statements, Basic logical connectives, conjunction, and disjunction, Negation, Conditional statements, The Contrapositive of conditional statements, the converse of conditional statements, Biconditional statements, Quantifiers, Validity of statements.
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