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# JEE Main Mathematics Syllabus: Topic-wise weightage, Best books

Latest Update: As announced by the HRD Minister Mr Ramesh Pokhriyal on 5th May, 2020, the JEE Main examination will be conducted from 18th – 23rd July, 2020.

JEE Main Mathematics Syllabus is prepared by the examination conducting body. NTA will release the syllabus along with the information brochure on JEE Main 2020. As per the analysis of previous years’ JEE Main papers, it is expected that there will be no change in the syllabus. However, there may be a change in the JEE Main Exam Pattern.

JEE Main Mathematics syllabus is based on the syllabus of class 11 and 12 of CBSE board. By knowing the JEE Main Mathematics Syllabus students will have clear idea about what type of questions asked in the paper, and difficulty level of the papers. Read the following article to no more about JEE Main syllabus for Mathematics section, weightage of chapters and number of questions from each unit.

## JEE Main Mathematics Syllabus

Following is the detailed analysis of unit wise and topic wise Mathematics syllabus:

### Unit 1: Sets, Relations and Functions

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

### Unit 2: Complex Number 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: Sequences 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: Co-ordinate 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.
• The distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of 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: Three Dimensional 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

• Vectors and scalars, the addition of vectors.
• Components of a vector in two dimensions and three-dimensional space.
• Scalar and vector products, scalar and vector triple product.

### Unit 14: Statistics and Probability

• Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
• Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

### Unit 15: Trigonometry

• Trigonometric identities and equations.
• Trigonometric functions.
• Inverse trigonometric functions and their properties.
• Heights and Distances

### Unit 16: Mathematical Reasoning

• Statements, logical operations and, or, implies, implied by, if and only if.
• Understanding of tautology, contradiction, converse, and Contrapositive

## JEE Main Mathematics Syllabus: Chapter-Wise Weightage

Some chapters from the JEE Main Mathematics syllabus carry more weightage than the others. The table provided below contains the most important topics from JEE Main syllabus with weightage:

 Important Topics Expected weightage Coordinate Geometry 12% Integral Calculus 12% Trigonometry 7% Sequence and Series 7% Matrices and Determinants 7% Differential Equations 7%

There are a total of 16 units in JEE Main Syllabus for Mathematics with the following weightage:

 Topic Number of questions Sets, Relations and Functions 1 Complex Numbers and Quadratic Equations 3 Matrices and Determinants 2 Permutations and Combinations 1 Mathematical Induction 1 Binomial Theorem and its simple applications 1 Sequences and Series 2 Limit, Continuity and Differentiability 1 Integral Calculus 3 Differential Equations 1 Co-Ordinate Geometry 5 Three Dimensional Geometry 3 Vector Algebra 1 Statistics and Probability 2 Trigonometry 2 Mathematical Reasoning 1

## Recommended Books for Preparing JEE Main Mathematics

Mathematics section requires a comprehensive preparation. The following table represents some of the best books for JEE Main along with their author’s name that students can prefer for their Mathematical exam preparation:

 Books Name Authors Name IIT Mathematics M.L. Khanna Differential Calculus Das Gupta Class XI and XII Mathematics R.D. Sharma Trigonometry, Geometry Books S.L. Loney Integral Calculus for IIT-JEE Amit Agarwal Calculus and Analytic Geometry Thomas and Finney Problems in Calculus of One Variable I. A. Maron Higher Algebra Hall and Knight

## Some Numerical Value Based Question in Mathematics

Q1. Let α and β be two roots of the equation x2+2x+2=0, then α 15+β15 is equal to_____________.

Ans. -256

Q2. Consider a group of 5 females and 7 males. The number of different teams consisting of 2 females and 3 males, that can be formed from this group, if there are two specific males A and B, who refuse to be the member of the same team, is ________________.

Ans. 300

Q3. If y = y (x) is the solution of the differential equation x +2y = x2 satisfying y (1) = 1, then 16 y (1/2) is equal to _______.

Ans. 49

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