Maths Syllabus for JEE Mains & Advanced – 2021

0
Join NEET Medical Exam Telegram Channel Click Here
Join IIT JEE Engg. Maths Telegram Channel Click Here
Join Physics Chemistry Biology Channel Click Here
Join Board & Class 11th & 12th Channel Click Here
Join Our Quiz for All Exam Channel Click Here

 

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:

JEE Main Maths Syllabus 2019

  • 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:

JEE Main Maths Syllabus 2019

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.

JEE Advanced Maths Syllabus

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.

 

Syllabus and Previous Year Papers

Chemistry Syllabus for NEET & AIIMS Exams Click Here
Chemistry Syllabus for JEE Mains & Advanced Click Here
Chapter Wise NEET Chemistry Syllabus Click Here
Physics Syllabus for NEET & AIIMS Exams Click Here
Physics Syllabus for JEE Mains & Advanced Click Here
Chapter Wise NEET Physics Syllabus Click Here
Biology Syllabus for NEET & AIIMS Exams Click Here
Chapter Wise NEET Biology Syllabus Click Here
Maths Syllabus for JEE Mains & Advanced Click Here
Download NEET Previous Year Question Papers with Solution Click Here

 

Please Support us Like & Share Our Social Network

Facebook   https://www.facebook.com/ExamsRoadOfficial
Telegram  https://telegram.me/ExamsRoad
Twitter  https://twitter.com/ExamsRoad
Instagram https://www.instagram.com/ExamsRoad/
YouTube  Click Here To Subscribe Now

 

Thank You.

By TEAM ExamsRoad.com

ExamsRoad

LEAVE A REPLY

Please enter your comment!
Please enter your name here