jee main 2013 mathematics syllabus
The careful JEE Main 2014 Mathematics Syllabus is as follows:
UNIT one : SETS, RELATIONS AND FUNCTIONS:
Sets and their representation; Union, intersection and complement of sets and their algebraical properties; Power set; Relation, varieties of relations, equivalence relations, functions;. one-one, into and onto functions, composition of functions.
JEE Main 2014 arithmetic programme
UNIT two : complicated NUMBERS AND QUADRATIC EQUATIONS:
Complex numbers as ordered pairs of reals, illustration of complicated numbers within the kind a+ib and their illustration in an exceedingly plane, Argand diagram, pure mathematics of complicated numbers, modulus and argument (or amplitude) of a fancy range, root of a fancy range, triangle difference, Quadratic equations in real and sophisticated number representation system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.
JEE Main 2014 arithmetic programme
UNIT three : MATRICES AND DETERMINANTS:
Matrices, pure mathematics of matrices, varieties of matrices, determinants and matrices of order 2 and 3. Properties of determinants, analysis of determinants, space of triangles victimisation determinants. Adjoint and analysis of inverse of a matrix victimisation determinants and elementary transformations, check of consistency and answer of coincidental linear equations in 2 or 3 variables victimisation determinants and matrices.
UNIT four : PERMUTATIONS AND COMBINATIONS:
Fundamental principle of enumeration, permutation as an appointment and combination as choice, which means of P (n,r) and C (n,r), easy applications.
JEE Main 2014 arithmetic programme
UNIT five : MATHEMATICAL INDUCTION:
Principle of Mathematical Induction and its easy applications.
UNIT half-dozen : theorem AND ITS easy APPLICATIONS:
Binomial theorem for a positive integral index, general term and term, properties of Binomial coefficients and straightforward applications.
JEE Main 2014 arithmetic programme
UNIT seven : SEQUENCES AND SERIES:
Arithmetic and Geometric progressions, insertion of arithmetic, geometric means that between 2 given numbers. Relation between A.M. and G.M. total upto n terms of special series: S n, S n2, Sn3. Arithmetico – progression.
UNIT eight : LIMIT, CONTINUITY AND DIFFERENTIABILITY:
Real – valued functions, pure mathematics of functions, polynomials, rational, pure mathematics, exponent and exponential functions, inverse functions. Graphs of easy functions. Limits, continuity and differentiability. Differentiation of the total, difference, product and quotient of 2 functions. Differentiation of pure mathematics, inverse pure mathematics, exponent, exponential, composite and implicit functions; derivatives of order upto 2. Rolle’s and Lagrange’s norm Theorems. Applications of derivatives: Rate of modification of quantities, monotonic – increasing and decreasing functions, Maxima and minima of functions of 1 variable, tangents and normals.
JEE Main 2014 arithmetic programme
UNIT nine : INTEGRAL CALCULUS:
Integral as associate degree opposing – spinoff. basic integrals involving algebraical, pure mathematics, exponential and exponent functions. Integration by substitution, by elements and by partial fractions. Integration victimisation pure mathematics identities.
Evaluation of easy integrals of the kind Integral as limit of a total. basic Theorem of Calculus. Properties of definite integrals. analysis of definite integrals, crucial areas of the regions finite by easy curves in customary kind.
JEE Main 2014 arithmetic programme
UNIT 10: DIFFERENTIAL EQUATIONS:
Ordinary differential equations, their order and degree. Formation of differential equations. answer of differential equations by the strategy of separation of variables, answer of consistent and linear differential equations of the type: dy/dx+p(x)y=q(x)
UNIT 11: CO-ORDINATE GEOMETRY:
Cartesian system of rectangular co-ordinates ten in an exceedingly plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.
JEE Main 2014 arithmetic programme
Straight lines
Various styles of equations of a line, intersection of lines, angles between 2 lines, conditions for concurrence of 3 lines, distance of a degree from a line, equations of internal and external bisectors of angles between 2 lines, coordinates of centre of mass, orthocentre and circumcentre of a triangle, equation of family of lines passing through the purpose of intersection of 2 lines.
JEE Main 2014 arithmetic programme
Circles, conic sections
Standard variety of equation of a circle, general variety of the equation of a circle, its radius and centre, equation of a circle once the tip points of a diameter square measure 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, conic and hyperbola) in customary forms, condition for y = Mx + c to be a tangent and purpose (s) of tangency.
UNIT 12: 3 DIMENSIONAL GEOMETRY:
Coordinates of a degree in house, distance between 2 points, section formula, direction ratios and direction cosines, angle between 2 crossed lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in several forms, intersection of a line and a plane, planar lines.
JEE Main 2014 arithmetic programme
UNIT 13: VECTOR ALGEBRA:
Vectors and scalars, addition of vectors, parts of a vector in 2 dimensions and 3 dimensional house, scalar and vector merchandise, scalar and vector triple product.
UNIT 14: STATISTICS AND PROBABILITY:
Measures of Dispersion: Calculation of mean, median, mode of sorted and ungrouped information calculation of ordinary deviation, variance and mean deviation from the mean for sorted and ungrouped information.
JEE Main 2014 arithmetic programme
Probability: chance of an incident, addition and multiplication theorems of chance, Baye’s theorem, chance distribution of a random variable, Bernoulli trials and distribution.
UNIT 15: TRIGONOMETRY:
Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances.
JEE Main 2014 arithmetic programme
UNIT 16: MATHEMATICAL REASONING:
Statements, logical operations and, or, implies, implied by, if and given that. Understanding of tautology, contradiction, converse and contrapositive.
JEE Main 2014 Exam Pattern
UNIT one : SETS, RELATIONS AND FUNCTIONS:
Sets and their representation; Union, intersection and complement of sets and their algebraical properties; Power set; Relation, varieties of relations, equivalence relations, functions;. one-one, into and onto functions, composition of functions.
JEE Main 2014 arithmetic programme
UNIT two : complicated NUMBERS AND QUADRATIC EQUATIONS:
Complex numbers as ordered pairs of reals, illustration of complicated numbers within the kind a+ib and their illustration in an exceedingly plane, Argand diagram, pure mathematics of complicated numbers, modulus and argument (or amplitude) of a fancy range, root of a fancy range, triangle difference, Quadratic equations in real and sophisticated number representation system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.
JEE Main 2014 arithmetic programme
UNIT three : MATRICES AND DETERMINANTS:
Matrices, pure mathematics of matrices, varieties of matrices, determinants and matrices of order 2 and 3. Properties of determinants, analysis of determinants, space of triangles victimisation determinants. Adjoint and analysis of inverse of a matrix victimisation determinants and elementary transformations, check of consistency and answer of coincidental linear equations in 2 or 3 variables victimisation determinants and matrices.
UNIT four : PERMUTATIONS AND COMBINATIONS:
Fundamental principle of enumeration, permutation as an appointment and combination as choice, which means of P (n,r) and C (n,r), easy applications.
JEE Main 2014 arithmetic programme
UNIT five : MATHEMATICAL INDUCTION:
Principle of Mathematical Induction and its easy applications.
UNIT half-dozen : theorem AND ITS easy APPLICATIONS:
Binomial theorem for a positive integral index, general term and term, properties of Binomial coefficients and straightforward applications.
JEE Main 2014 arithmetic programme
UNIT seven : SEQUENCES AND SERIES:
Arithmetic and Geometric progressions, insertion of arithmetic, geometric means that between 2 given numbers. Relation between A.M. and G.M. total upto n terms of special series: S n, S n2, Sn3. Arithmetico – progression.
UNIT eight : LIMIT, CONTINUITY AND DIFFERENTIABILITY:
Real – valued functions, pure mathematics of functions, polynomials, rational, pure mathematics, exponent and exponential functions, inverse functions. Graphs of easy functions. Limits, continuity and differentiability. Differentiation of the total, difference, product and quotient of 2 functions. Differentiation of pure mathematics, inverse pure mathematics, exponent, exponential, composite and implicit functions; derivatives of order upto 2. Rolle’s and Lagrange’s norm Theorems. Applications of derivatives: Rate of modification of quantities, monotonic – increasing and decreasing functions, Maxima and minima of functions of 1 variable, tangents and normals.
JEE Main 2014 arithmetic programme
UNIT nine : INTEGRAL CALCULUS:
Integral as associate degree opposing – spinoff. basic integrals involving algebraical, pure mathematics, exponential and exponent functions. Integration by substitution, by elements and by partial fractions. Integration victimisation pure mathematics identities.
Evaluation of easy integrals of the kind Integral as limit of a total. basic Theorem of Calculus. Properties of definite integrals. analysis of definite integrals, crucial areas of the regions finite by easy curves in customary kind.
JEE Main 2014 arithmetic programme
UNIT 10: DIFFERENTIAL EQUATIONS:
Ordinary differential equations, their order and degree. Formation of differential equations. answer of differential equations by the strategy of separation of variables, answer of consistent and linear differential equations of the type: dy/dx+p(x)y=q(x)
UNIT 11: CO-ORDINATE GEOMETRY:
Cartesian system of rectangular co-ordinates ten in an exceedingly plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.
JEE Main 2014 arithmetic programme
Straight lines
Various styles of equations of a line, intersection of lines, angles between 2 lines, conditions for concurrence of 3 lines, distance of a degree from a line, equations of internal and external bisectors of angles between 2 lines, coordinates of centre of mass, orthocentre and circumcentre of a triangle, equation of family of lines passing through the purpose of intersection of 2 lines.
JEE Main 2014 arithmetic programme
Circles, conic sections
Standard variety of equation of a circle, general variety of the equation of a circle, its radius and centre, equation of a circle once the tip points of a diameter square measure 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, conic and hyperbola) in customary forms, condition for y = Mx + c to be a tangent and purpose (s) of tangency.
UNIT 12: 3 DIMENSIONAL GEOMETRY:
Coordinates of a degree in house, distance between 2 points, section formula, direction ratios and direction cosines, angle between 2 crossed lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in several forms, intersection of a line and a plane, planar lines.
JEE Main 2014 arithmetic programme
UNIT 13: VECTOR ALGEBRA:
Vectors and scalars, addition of vectors, parts of a vector in 2 dimensions and 3 dimensional house, scalar and vector merchandise, scalar and vector triple product.
UNIT 14: STATISTICS AND PROBABILITY:
Measures of Dispersion: Calculation of mean, median, mode of sorted and ungrouped information calculation of ordinary deviation, variance and mean deviation from the mean for sorted and ungrouped information.
JEE Main 2014 arithmetic programme
Probability: chance of an incident, addition and multiplication theorems of chance, Baye’s theorem, chance distribution of a random variable, Bernoulli trials and distribution.
UNIT 15: TRIGONOMETRY:
Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances.
JEE Main 2014 arithmetic programme
UNIT 16: MATHEMATICAL REASONING:
Statements, logical operations and, or, implies, implied by, if and given that. Understanding of tautology, contradiction, converse and contrapositive.
JEE Main 2014 Exam Pattern