# JEE Advanced Syllabus

JEE Advanced is the later stage of JEE which a student reaches after clearing the JEE Main exam. Although the cumulative preparation of both the stages start very early from 11th class or even earlier. However, the syllabus of JEE advanced is slightly different from that of JEE main syllabus. The questions asked in JEE advanced are strictly based on the topics given in the syllabus. Hence, it is always advantageous to read the syllabus carefully beforehand.

The syllabus for JEE Advanced is divided into 3 parts-

• Physics
• Chemistry
• Maths

## JEE advanced syllabus: Maths

The syllabus for JEE Advanced Maths is broadly divided into 8 different units. These are as follows-

 UNITS TOPICS Algebra 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 with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots. Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic m eans, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers. 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, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skewsymmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables. Probability Addition and m ultiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations. Trigonometry Trigonometric functions, their periodicity and graphs, addition and formulae involving multiple and subsubtraction formulae, multiple angles, general solution of trigonometric equations. Relations between sides and angles of a triangle, sine rule, cosine rule, half and the area of a triangle, inverse trigonangle formula ometric functions (principal value only) 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 p roblems. Three dimensions : Direction cosines and direction ratios, equation of a strai space, equation of a plane, distance of a point from a plane. Differential calculus 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. 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 func tions. Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions. Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, de rivatives 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 a nd decreasing functions, maximum and minimum values of a function, Rolle’s theorem and Lagrange’s mean value theorem. Integral calculus Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their prope c alculus. rties, fundamental theorem of integral Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves. Formation of or dinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations. Vectors Addition of vectors, scalar multiplication, dot and cross products, scalar triple products an d their geometrical interpretations.

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