JEE Main is very important engineering entrance exam for aspirants, who are seeking for government engineering college for higher education. we have done a research from 2013 to 2015 on Maths question paper of Joint entrance examination (main) and also from official information bulletin of (jeemain.nic.in) and find most important topics and chapters.

JEE Main Maths Syllabus is given below:

Algebra: Sets relations & functions, De-Morgan's Law, Mapping Inverse relations, Equivalence relations, Peano's axioms, Definition of rationals and integers through equivalence relation, Indices and surds, Solutions of simultaneous and quadratic equations, A.P., G.P. and H.P., Special sums i.e. Un2 and Un3 (nUN ), Partial fraction, Binomial theorem for any index, exponential series, Logarithm and Logarithmic series. Determinants and their use in solving simultaneous linear equations, Matrices, Algebra of matrices, Inverse of a matrix, Use of matrix for solving equations.

Probability: Definition, Dependent and independent events, Numerical problem on addition and

multiplication, theorem of probability.

Trigonometry: Identities, Trigonometric equations, properties of triangles, solution of triangles, heights and distances, Inverse function, Complex numbers and their properties, Cube roots of unity, De-Moivre's theorem.

Co-ordinate Geometry: Pair of straight lines, Circles, General equation of second degree, parabola, ellipse and hyperbola, tracing of conics.

Calculus: Limits & continuity of functions, Differentiation of function of function, tangents & normal, Simple examples of Maxima & Minima, Indeterminate forms, Integration of function by parts, by substitution and by partial fraction, definite integral, application to volumes and surfaces of frustums of sphere, cone and cylinder. Differential equations of first order and of first degree.

Vectors : Algebra of vectors, scalar and vector products of two and three vectors and their applications.

Dynamics : Velocity, composition of velocity, relative velocity, acceleration, composition of accelerations, Motion under gravity, Projectiles, Laws of motion, Principles of conservation of momentum and energy, direct impact of smooth bodies.

Statics: Composition of coplanar, concurrent and parallel forces moments and couples resultant of set of coplanar forces and condition of equilibrium, determination of centroid in simple cases, Problems involving friction.

Complex Numbers: Complex number system - conjugate, properties, ordered pair

representation. Modulus – properties, geometrical representation, polar form,

principal value, conjugate, sum, difference, product, quotient, vector interpretation, solutions of polynomial equations, De-Moivre’s theorem and its applications. Roots of a complex number - nth roots, cube roots, fourth roots.

Differential Calculus: Derivative as a rate measurer - rate of change, velocity,

acceleration, related rates, derivative as a measure of slope, tangent, normal and angle between curves, maxima and minima. Mean value theorem - Rolle’s Theorem, Lagrange Mean Value

Theorem, Taylor’s and Maclaurin’s series, L’ Hospital’s Rule, stationary points, increasing, decreasing, maxima, minima, concavity, convexity and points of inflexion.

Errors and approximations – absolute, relative, percentage errors - curve tracing, partial derivatives, Euler’s theorem.

Differential Equations: Differential equations - formation of differential equations,

order and degree, solving differential equations (1st order), variables separable, homogeneous and linear equations. Second order linear differential equations - second order linear

differential equations with constant co-efficients, finding the particular integral if f (x) = emx, sin mx, cos mx, x, x2.

JEE Main Maths Syllabus is given below:

Algebra: Sets relations & functions, De-Morgan's Law, Mapping Inverse relations, Equivalence relations, Peano's axioms, Definition of rationals and integers through equivalence relation, Indices and surds, Solutions of simultaneous and quadratic equations, A.P., G.P. and H.P., Special sums i.e. Un2 and Un3 (nUN ), Partial fraction, Binomial theorem for any index, exponential series, Logarithm and Logarithmic series. Determinants and their use in solving simultaneous linear equations, Matrices, Algebra of matrices, Inverse of a matrix, Use of matrix for solving equations.

Probability: Definition, Dependent and independent events, Numerical problem on addition and

multiplication, theorem of probability.

Trigonometry: Identities, Trigonometric equations, properties of triangles, solution of triangles, heights and distances, Inverse function, Complex numbers and their properties, Cube roots of unity, De-Moivre's theorem.

Co-ordinate Geometry: Pair of straight lines, Circles, General equation of second degree, parabola, ellipse and hyperbola, tracing of conics.

Calculus: Limits & continuity of functions, Differentiation of function of function, tangents & normal, Simple examples of Maxima & Minima, Indeterminate forms, Integration of function by parts, by substitution and by partial fraction, definite integral, application to volumes and surfaces of frustums of sphere, cone and cylinder. Differential equations of first order and of first degree.

Vectors : Algebra of vectors, scalar and vector products of two and three vectors and their applications.

Dynamics : Velocity, composition of velocity, relative velocity, acceleration, composition of accelerations, Motion under gravity, Projectiles, Laws of motion, Principles of conservation of momentum and energy, direct impact of smooth bodies.

Statics: Composition of coplanar, concurrent and parallel forces moments and couples resultant of set of coplanar forces and condition of equilibrium, determination of centroid in simple cases, Problems involving friction.

Complex Numbers: Complex number system - conjugate, properties, ordered pair

representation. Modulus – properties, geometrical representation, polar form,

principal value, conjugate, sum, difference, product, quotient, vector interpretation, solutions of polynomial equations, De-Moivre’s theorem and its applications. Roots of a complex number - nth roots, cube roots, fourth roots.

Differential Calculus: Derivative as a rate measurer - rate of change, velocity,

acceleration, related rates, derivative as a measure of slope, tangent, normal and angle between curves, maxima and minima. Mean value theorem - Rolle’s Theorem, Lagrange Mean Value

Theorem, Taylor’s and Maclaurin’s series, L’ Hospital’s Rule, stationary points, increasing, decreasing, maxima, minima, concavity, convexity and points of inflexion.

Errors and approximations – absolute, relative, percentage errors - curve tracing, partial derivatives, Euler’s theorem.

Differential Equations: Differential equations - formation of differential equations,

order and degree, solving differential equations (1st order), variables separable, homogeneous and linear equations. Second order linear differential equations - second order linear

differential equations with constant co-efficients, finding the particular integral if f (x) = emx, sin mx, cos mx, x, x2.