JEE Main Syllabus 2019 – Detailed Syllabus for Mathematics

Published on : 20th June 2018
IIT JEE Main Exam

Earlier known as AIEEE (All India Engineering Entrance Examination), Joint Entrance Examination (JEE) Main is an all-India entrance examination conducted by NTA (previously regulated by CBSE). Candidates looking to get into India’s leading engineering institutes like IITs, NITs, IITs, GFTIs and IIEST must clear the entrance test with good score. Qualified candidates will be ranked on both state and all-India basis. They will receive AIR (All India Rank), and SR (State Rank) ranks as per their score. To help them crack the exam, we have furnished the detailed syllabus for Mathematics subject. The JEE Main 2019 Mathematics syllabus will tell you what topics or chapters the candidates should cover. 

JEE Main Mathematics Syllabus 2019:

The syllabus of maths mainly comprises topics from Classes 11th and 12th. Students who have done well in the math paper in their board exams would find the chapters quite easy. The JEE Main mathematic syllabus 2019 covers 16 Units. They are mentioned underneath:

Units

Chapters

UNIT 1: SETS, RELATIONS AND FUNCTIONS

Sets and their representation; one-one, into and onto functions, a composition of functions; Power set; Relation, Types of relations, equivalence relations, functions; Union, intersection and complement of sets and their algebraic properties.

UNIT 2: COMPLEX NUMBERS AND QUADRATIC EQUATIONS

Representation of complex numbers in the form a+ib and their representation in a plane, Complex numbers as ordered pairs of reals, Quadratic equations in complex and real number system and their solutions, Argand diagram, algebra of complex numbers, square root of a complex number, modulus and argument (or amplitude) of a complex number, triangle inequality. The formation of quadratic equations with given roots, the relation between roots and coefficients, nature of roots.

UNIT 3: MATRICES AND DETERMINANTS

Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Properties of determinants, evaluation of determinants, an area of triangles using determinants. Test of consistency and solution of simultaneous linear equations in two/three variables using determinants and matrices.

UNIT 4: PERMUTATIONS AND COMBINATIONS

Meaning of P (n,r) and C (n,r), simple applications, the Fundamental principle of counting, permutation as an arrangement and combination as a selection.

UNIT 5: MATHEMATICAL INDUCTION

Principle of Mathematical Induction and applications

UNIT 6: BINOMIAL THEOREM

Binomial theorem for a positive integral index, general term and middle term, Binomial coefficients properties and applications.

UNIT 7: SEQUENCES AND SERIES

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Sum up to n terms of special series: S n, S n2, S n3. Arithmetic-Geometric progression. The relation between A.M. and G.M.

UNIT 8: LIMIT, CONTINUITY AND DIFFERENTIABILITY

Real-valued functions, logarithmic and exponential functions, trigonometric, polynomials, rational, algebra of functions, inverse functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Graphs of simple functions. Rolle’s and Lagrange’s Mean Value Theorems. Inverse trigonometric, differentiation of trigonometric, exponential, logarithmic, composite and implicit functions; derivatives of order up to two. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, tangents and normal, Maxima and minima of functions of one variable.

UNIT 9: INTEGRAL CALCULUS

Fundamental integrals involving algebraic, exponential, trigonometric and logarithmic functions. Integral as an antiderivative. Integration by parts and by partial fractions, by substitution. Integration using trigonometric identities. Fundamental Theorem of Calculus. Integral as limit of a sum. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form. Properties of definite integrals.

UNIT 10: DIFFERENTIAL EQUATIONS

Ordinary differential equations, degree and order. The solution of differential equations by the method of separation of variables, the solution of homogeneous and linear differential equations. Formation of differential equations.

UNIT 11: CO-ORDINATE GEOMETRY

Cartesian system of rectangular co-ordinates in a plane, locus and its equation, distance formula, translation of axes, section formula, intercepts of a line on the coordinate axes, the slope of a line, parallel and perpendicular lines.

Straight lines

Various forms of equations of a line, angles between two lines, intersection of lines, distance of a point from a line, conditions for concurrence of three lines, equations of internal and external bisectors of angles between two lines, equation of family of lines passing through the point of intersection of two lines, coordinates of centroid, orthocentre and circumcentre of a triangle.

Circles, conic sections

General form of the equation of a circle, its radius and centre, standard form of equation of a circle, 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 a circle when the endpoints of a diameter are given, equation of the tangent. Equations of conic sections (parabola, ellipse and hyperbola) in standard forms, sections of cones, condition for y = mx + c to be a tangent and point (s) of tangency.

UNIT 12: THREE DIMENSIONAL GEOMETRY

Coordinates of a point in space, the distance between two points, direction ratios and direction cosines, section formula, an angle between two intersecting lines. Equations of a plane and a line in different forms, an intersection of a plane and a line, coplanar lines. Skew lines, the shortest distance between them and its equation.

UNIT 13: VECTOR ALGEBRA

An addition of vectors, scalars and vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector triple product, scalar and vector products.

UNIT 14: STATISTICS AND PROBABILITY

Measures of Dispersion

Calculation of standard deviation, mean deviation and variance for grouped and ungrouped data. Calculation of mean, median, mode of grouped and ungrouped data. 

Probability

Baye’s theorem, the probability distribution of a random variate, Probability of an event, addition and multiplication theorems of probability, Binomial distribution and Bernoulli trials.

UNIT 15: TRIGONOMETRY

Trigonometrical equations and identities. Trigonometrical functions. Heights and Distances. Inverse trigonometrical functions and properties.

UNIT 16: MATHEMATICAL REASONING

Statements, logical operations or implies. Understanding of converse, contradiction, tautology and contrapositive.

There are two papers – Paper I and Paper II – for the Joint Entrance Examination Main.

  • The Paper I is conducted for the B.Tech/B.E aspirants.
  • The Paper II is held for the B.Planning/B.Arch programmes.

From the academic year 2019, the National Testing Agency will regulate the Joint Entrance Examination Main two times in a year (January and April). Students are allowed to take both the exams; the scorecard that would get the highest marks would be considered for admission into the elite technical colleges.

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