Every year more than one lakh students appear in the IIT JEE examination. In India as well as internationally it has been recognized as one of the most important examinations for the students who want to pursue theircareers in the Engineering field**.** JEE exam is the way to get admission to the best engineering colleges in India. Those who pass the **JEE Main exam** will be eligible for admission to some of the best colleges in the country since the exam’s results are accepted. Those who pass JEE Main will be able to take the **JEE Advanced exam**, which is the second round of the exam. Those who succeed in JEE Advanced will be admitted to one of the IITs.

JEE (Joint Entrance Examination) is a competitive entrance exam administered by the National Testing Agency (NTA) for admission to India’s top engineering institutes and universities. It is divided into two phases: JEE Main and JEE Advanced, with an objective pattern and a syllabus of **Physics, Chemistry, and Maths (PCM)** from** 11th and 12th grades**. Previously, it was known as AIEEE (All India Engineering Entrance Examination). Learn about the differences between AIEEE and JEE Main.

The distinction between Jee Main and Advanced is as follows:

**JEE Main**: Selected/top/qualified candidates in JEE Main are entitled to participate/write in JEE Advanced as a qualifying exam for admission to IITs, NITs, and Centrally Funded Technical Institutes (CFTIs) or other engineering institutes.**JEE Advanced:**This exam is used to select students for elite/premier IITs and NITs.

After a thorough discussion of the educational panel changes in the **JEE Mains syllabus 2023** which are finally decided are as follows:

Statistics is a new **Chapter in the JEE Advanced mathematics syllabus 2023**. Instead, the triangle’s solution has been removed from the curriculum. Semiconductors and communications are not covered in physics; however, a few JEE Main topics, including forced and damped oscillations, EM waves, and polarisation, have been introduced.

**Sets, Relations and Functions:**

Sets and their representations, different kinds of sets (empty, finite and infinite), algebra of sets, intersection, complement, difference and symmetric difference of sets and their algebraic properties, De-Morgan’s laws on union, intersection, difference (for finite number of sets) and practical problems based on them.

Cartesian product of finite sets, ordered pair, relations, domain and codomain of relations, equivalence relation

Function as a special case of relation, functions as mappings, domain, codomain, range of functions, invertible functions, even and odd functions, into, onto and one-to-one functions, special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer etc.), sum, difference, product and composition of functions.

**Algebra:**

Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.

Statement of fundamental theorem of algebra, Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.

Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite arithmetic and geometric progressions, infinite geometric series, sum of the first n natural numbers, sums of squares and cubes of the first n natural numbers.

Logarithms and their properties, permutations and combinations, binomial theorem for a positive integral index, properties of binomial coefficients.

**Matrices**

Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, elementary row and column transformations, determinant of a square matrix of order up to three, adjoint of a matrix, 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 and Statistics**

Random experiment, sample space, different types of events (impossible, simple, compound), addition and multiplication rules of probability, conditional probability, independence of events, total probability, Bayes Theorem, computation of probability of events using permutations and combinations.

Measure of central tendency and dispersion, mean, median, mode, mean deviation, standard deviation and variance of grouped and ungrouped data, analysis of the frequency distribution with same mean but different variance, random variable, mean and variance of the random variable.

**Trigonometry:**

Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations. Inverse trigonometric functions (principal value only) and their elementary properties.

**Analytical Geometry**

Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.

Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; Centroid, orthocentre, incentre and circumcentre of a triangle.

Equation of a circle in various forms, equations of tangent, normal and chord. Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the

points of intersection of two circles and those of a circle and a straight line. Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal.

Locus problems.

Three dimensions: Distance between two points, direction cosines and direction ratios, equation of a straight line in space, skew lines, shortest distance between two lines, equation of a plane, distance of a point from a plane, angle between two lines, angle between two planes, angle between a line and the plane, coplanar lines.

**Differential Calculus**

Limit of a function at a real number, 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.

Continuity of composite functions, intermediate value property of continuous functions. Derivative of a function, a derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.

Tangents and normals, increasing and decreasing functions, derivatives of order two, maximum and minimum values of a function, Rolle’s theorem and Lagrange’s mean value theorem, geometric interpretation of the two theorems, derivatives up to order two of implicit functions, geometric interpretation of derivatives.

**Integral Calculus**

Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals as the limit of sums, definite integrals and their properties, fundamental theorem of integral calculus.

Integration by parts, integration by the methods of substitution and partial fractions, and application of definite integrals to the determination of areas bounded by simple curves. Formation of ordinary differential equations, solution of homogeneous differential equations of the first order and first degree, separation of variables method, linear first-order differential equations.

**Vectors**

Addition of vectors, scalar multiplication, dot and cross products, scalar and vector triple products, and their geometrical interpretations.

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