# Maths Syllabus for JEE Mains & Advanced – 2021

0
Contents

## Maths Syllabus for JEE

 Unit 1: Sets, Relations, and Functions Sets and their representation. Union, intersection, and complement of sets and their algebraic properties. Powerset. Relation, Types of relations, equivalence relations. Functions; one-one, into and onto functions, the composition of functions. Unit 2: Complex Numbers and Quadratic Equations Complex numbers as ordered pairs of reals. Representation of complex numbers in the form (a+ib) and their representation in a plane, Argand diagram. Algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number. Triangle inequality. Quadratic equations in real and complex number system and their solutions. The relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots. Unit 3: Matrices and Determinants Matrices: Algebra of matrices, types of matrices, and matrices of order two and three. Determinants: Properties of determinants, evaluation of determinants, the area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations. Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices. Unit 4: Permutations and Combinations The fundamental principle of counting. Permutation as an arrangement and combination as selection. The meaning of P (n,r) and C (n,r). Simple applications. Unit 5: Mathematical Induction The principle of Mathematical Induction and its simple applications. Unit 6: Binomial Theorem Binomial theorem for a positive integral index. General term and middle term. Properties of Binomial coefficients and simple applications. Unit 7: Sequence and Series Arithmetic and Geometric progressions, insertion of arithmetic. Geometric means between two given numbers. The relation between A.M. and G.M. Sum up to n terms of special series: Sn, Sn2, Sn3. Arithmetic Geometric progression. Unit 8: Limit, Continuity and Differentiability Real-valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity, and differentiability. Differentiation of the sum, difference, product, and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order up to two. Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic increasing and decreasing functions, Maxima, and minima of functions of one variable, tangents, and normals. Unit 9: Integral Calculus Integral as an antiderivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts, and by partial fractions. Integration using trigonometric identities. Integral as limit of a sum. Evaluation of simple integrals: Fundamental Theorem of Calculus. Properties of definite integrals, evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form. Unit 10: Differential Equations Ordinary differential equations, their order, and degree. Formation of differential equations. The solution of differential equations by the method of separation of variables. The solution of homogeneous and linear differential equations of the type: Unit 11: Coordinate Geometry Cartesian system of rectangular coordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, the slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes. Straight lines: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines. Distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of the centroid, orthocentre, and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines. Circles, conic sections: Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent. Sections of cones, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency. Unit 12: 3D Geometry Coordinates of a point in space, the distance between two points. Section formula, direction ratios and direction cosines, the angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines. Unit 13: Vector Algebra Scalars and Vectors. Addition, subtraction, multiplication and division of vectors. Vector’s Components in 2D and 3D space. Scalar products and vector products, triple product. Unit 14: Statistics and Probability Measures of Dispersion: Calculation of mean, mode, median, variance, standard deviation, and mean deviation of ungrouped and grouped data. Probability: Probability of events, multiplication theorems, addition theorems, Baye’s theorem, Bernoulli trials, Binomial distribution and probability distribution. Unit 15: Trigonometry Identities of Trigonometry and Trigonometric equations. Functions of Trigonometry. Properties of Inverse trigonometric functions. Problems on Heights and Distances. Unit 16v Mathematical Reasoning Statements and logical operations: or, and, implied by, implies, only if and if. Understanding of contradiction, tautology, contrapositive and converse.

 Unit 1 Algebra Complex Numbers Algebra of complex numbers, addition, multiplication, conjugation. Polar representation, properties of modulus and principal argument. Triangle inequality, cube roots of unity. Geometric interpretations. Quadratic Equations Quadratic equations with real coefficients. Relations between roots and coefficients. Formation of quadratic equations with given roots. Symmetric functions of roots. Sequence and Series Arithmetic, geometric, and harmonic progressions. Arithmetic, geometric, and harmonic means. Sums of finite arithmetic and geometric progressions, infinite geometric series. Sums of squares and cubes of the first n natural numbers. Logarithms Logarithms and their properties. Permutation and Combination Problems on permutations and combinations. Binomial Theorem Binomial theorem for a positive integral index. Properties of binomial coefficients. Matrices and Determinants Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix. Determinant of a square matrix of order up to three, the inverse of a square matrix of order up to three. Properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties. Solutions of simultaneous linear equations in two or three variables. Probability Addition and multiplication rules of probability, conditional probability. Bayes Theorem, independence of events. Computation of probability of events using permutations and combinations. Unit 2 Trigonometry Trigonometric Functions Trigonometric functions, their periodicity, and graphs, addition and subtraction formulae. Formulae involving multiple and submultiple angles. The general solution of trigonometric equations. Inverse Trigonometric Functions Relations between sides and angles of a triangle, sine rule, cosine rule. Half-angle formula and the area of a triangle. Inverse trigonometric functions (principal value only). Unit 3 Vectors Properties of Vectors The addition of vectors, scalar multiplication. Dot and cross products. Scalar triple products and their geometrical interpretations. Unit 4 Differential Calculus Functions Real-valued functions of a real variable, into, onto and one-to-one functions. Sum, difference, product, and quotient of two functions. Composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions. Even and odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions. Limits and Continuity Limit and continuity of a function. Limit and continuity of the sum, difference, product and quotient of two functions. L’Hospital rule of evaluation of limits of functions. Derivatives The derivative of a function, the derivative of the sum, difference, product and quotient of two functions. Chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions. Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative. Tangents and normals, increasing and decreasing functions, maximum and minimum values of a function. Rolle’s Theorem and Lagrange’s Mean Value Theorem. Unit 5 Integral calculus Integration Integration as the inverse process of differentiation. Indefinite integrals of standard functions, definite integrals, and their properties. Fundamental Theorem of Integral Calculus. Integration by parts, integration by the methods of substitution and partial fractions. Application of Integration Application of definite integrals to the determination of areas involving simple curves. Differential Equations Formation of ordinary differential equations. The solution of homogeneous differential equations, separation of variables method. Linear first-order differential equations.

Thank You.