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# JEE Main Paper 2 Syllabus ## JEE Main Paper 2 (B.Arch) Maths Syllabus

 UNIT 1 Sets, Relations and Functions Sets and their representation: Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Type of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions. UNIT 2 Complex Numbers 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 number, modulusand argument (or amplitude) of a complex number, triangle inequality, Quadratic equations inreal and complex number system and their solutions Relations between roots and co-efficient,nature of roots, the formation of quadratic equations with given roots. UNIT 3 Matrices and Determinants Matrices, algebra of matrices, type of matrices, determinants, and matrices of order two andthree, properties of determinants, evaluation of determinants, area of triangles using determinants, Adjoint, and evaluation of inverse of a square matrix using determinants andelementary transformations, Test of consistency and solution of simultaneous linear equationsin two or three variables using determinants and matrices. UNIT 4 Permutations and Combinations The fundamental principle of counting, permutation as an arrangement and combination assection, Meaning of P (n,r) and C (n,r), simple applications. UNIT 5 Mathematical Induction Principle of Mathematical Induction and its simple applications. UNIT 6 Binomial Theorem and its Simple Applications Binomial theorem for a positive integral index, general term and middle term, properties ofBinomial coefficients, and simple applications. UNIT 7 Sequences and Series Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M sum up to n terms of special series; Sn, Sn2, Sn3. Arithmetico-Geometric progression. UNIT 8 Limit, Continuity and Differentiability Real–valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic,and exponential functions, inverse function. 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 Meanvalue Theorems, Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable, tangentsand normal. UNIT 9 Integral Calculus Integral as an anti-derivative, Fundamental Integrals involving algebraic, trigonometric,exponential, and logarithms functions. Integrations by substitution, by parts, and by partial functions. Integration using trigonometric identities.Integral as limit of a sum. The fundamental theorem of calculus, properties of definite integrals.Evaluation of definite integrals, determining areas of the regions bounded by simple curves instandard form. UNIT 10 Differential Equations Ordinary differential equations, their order, and degree, the formation of differential equations,solution of differential equation by the method of separation of variables, solution of ahomogeneous and linear differential equation UNIT 11 Co-ordinate Geometry Cartesian system of rectangular coordinates 10 in a plane, distance formula, sections formula,locus, and its equation, translation of axis, slop of a line, parallel and perpendicular lines, intercept of a line on the co-ordinate axes. Straight lineVarious forms of equations of a line, intersection of lines, angles between two lines, conditionsfor concurrence of three lines, the distance of a point form a line, equations of internal andexternal by sectors of angles between two lines co-ordinate of the centroid, orthocentre, andcircumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines. Circle, conic sectionsA standard form of equations of a circle, the general form of the equation of a circle, its radiusand central, 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 betangent to a circle, equation of the tangent, sections of conics, equations of conic sections(parabola, ellipse, and hyperbola) in standard forms, condition for Y = mx + c to be a tangentand point (s) of tangency. UNIT 12 Three Dimensional Geometry Coordinates of a point in space, the distance between two points, section formula, directionsratios, direction cosines, the angle between two intersecting lines. Skew lines, the shortestdistance between them, and its equation. Equations of a line and a plane in different forms, theintersection 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 andthree-dimensional space, scalar and vector products, scalar and vector triple product. UNIT 14 Statistics and Probability Measures of discretion; calculation of mean, median, mode of grouped and ungrouped datacalculation of standard deviation, variance and mean deviation for grouped and ungroupeddata.Probability: Probability of an event, addition and multiplication theorems of probability, Baye'stheorem, probability distribution of a random variate, Bernoulli trials, and binomial distribution. UNIT 15 Trigonometry Trigonometrical identities and equations, trigonometrical functions, inverse trigonometricalfunctions, and their properties, heights, and distance. UNIT 16 Mathematical Reasoning Statement logical operations and, or, implies, implied by, if and only if, understanding oftautology, contradiction, converse, and contrapositive.

## JEE Main Paper 2 (B.Arch) Aptitude Test Syllabus

 UNIT 1 Awareness of persons, buildings, materials. Objects, texture related to Architecture and build environment. Visualizing three - dimensional objects from two dimensional drawings. Visualizing different sides of three dimensional objects. Analytical Reasoning Mental Ability (Visual, Numerical and Verbal) UNIT 2 Three dimensional perception: Understanding and appreciation of scale and proportions of objects, builing forms and elements, colour, texture, harmony and contrast. Design and drawing of geometrical or abstract shapes and patterns in pencil. Transformation of forms both 2D and 3D union, subtraction, rotation, development of surfaces and volumes. Generation of plans, elevations, and 3D views of objects. Creating 2-Dimensional and 3-Dimensional compositions using given shapes and forms.

## JEE Main Paper 2 (B.Arch) Drawing Syllabus

Sketching of scenes and activities from memory of urbanscape ( public space, market, festivals, street scenes, monuments, recreational spaces etc.), landscape ( riverfront's, jungles, gardens, trees, plants etc.) and rural life.

## JEE Main Paper 2 (B.Planning) Maths Syllabus

 UNIT 1 Sets, Relations and Functions Sets and their representation: Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Type of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions. UNIT 2 Complex Numbers 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 number, modulusand argument (or amplitude) of a complex number, triangle inequality, Quadratic equations inreal and complex number system and their solutions Relations between roots and co-efficient,nature of roots, the formation of quadratic equations with given roots. UNIT 3 Matrices and Determinants Matrices, algebra of matrices, type of matrices, determinants, and matrices of order two andthree, properties of determinants, evaluation of determinants, area of triangles using determinants, Adjoint, and evaluation of inverse of a square matrix using determinants andelementary transformations, Test of consistency and solution of simultaneous linear equationsin two or three variables using determinants and matrices. UNIT 4 Permutations and Combinations The fundamental principle of counting, permutation as an arrangement and combination assection, Meaning of P (n,r) and C (n,r), simple applications. UNIT 5 Mathematical Induction Principle of Mathematical Induction and its simple applications. UNIT 6 Binomial Theorem and its Simple Applications Binomial theorem for a positive integral index, general term and middle term, properties ofBinomial coefficients, and simple applications. UNIT 7 Sequences and Series Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M sum up to n terms of special series; Sn, Sn2, Sn3. Arithmetico-Geometric progression. UNIT 8 Limit, Continuity and Differentiability Real–valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic,and exponential functions, inverse function. 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 Meanvalue Theorems, Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable, tangentsand normal. UNIT 9 Integral Calculus Integral as an anti-derivative, Fundamental Integrals involving algebraic, trigonometric,exponential, and logarithms functions. Integrations by substitution, by parts, and by partial functions. Integration using trigonometric identities.Integral as limit of a sum. The fundamental theorem of calculus, properties of definite integrals.Evaluation of definite integrals, determining areas of the regions bounded by simple curves instandard form. UNIT 10 Differential Equations Ordinary differential equations, their order, and degree, the formation of differential equations,solution of differential equation by the method of separation of variables, solution of ahomogeneous and linear differential equation UNIT 11 Co-ordinate Geometry Cartesian system of rectangular coordinates 10 in a plane, distance formula, sections formula,locus, and its equation, translation of axis, slop of a line, parallel and perpendicular lines, intercept of a line on the co-ordinate axes. Straight lineVarious forms of equations of a line, intersection of lines, angles between two lines, conditionsfor concurrence of three lines, the distance of a point form a line, equations of internal andexternal by sectors of angles between two lines co-ordinate of the centroid, orthocentre, andcircumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines. Circle, conic sectionsA standard form of equations of a circle, the general form of the equation of a circle, its radiusand central, 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 betangent to a circle, equation of the tangent, sections of conics, equations of conic sections(parabola, ellipse, and hyperbola) in standard forms, condition for Y = mx + c to be a tangentand point (s) of tangency. UNIT 12 Three Dimensional Geometry Coordinates of a point in space, the distance between two points, section formula, directionsratios, direction cosines, the angle between two intersecting lines. Skew lines, the shortestdistance between them, and its equation. Equations of a line and a plane in different forms, theintersection 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 andthree-dimensional space, scalar and vector products, scalar and vector triple product. UNIT 14 Statistics and Probability Measures of discretion; calculation of mean, median, mode of grouped and ungrouped datacalculation of standard deviation, variance and mean deviation for grouped and ungroupeddata.Probability: Probability of an event, addition and multiplication theorems of probability, Baye'stheorem, probability distribution of a random variate, Bernoulli trials, and binomial distribution. UNIT 15 Trigonometry Trigonometrical identities and equations, trigonometrical functions, inverse trigonometricalfunctions, and their properties, heights, and distance. UNIT 16 Mathematical Reasoning Statement logical operations and, or, implies, implied by, if and only if, understanding oftautology, contradiction, converse, and contrapositive.

## JEE Main Paper 2 (B.Planning)Aptitude Test Syllabus

 UNIT 1 Awareness of persons, buildings, materials. Objects, texture related to Architecture and build environment. Visualizing three - dimensional objects from two dimensional drawings. Visualizing different sides of three dimensional objects. Analytical Reasoning Mental Ability (Visual, Numerical and Verbal) UNIT 2 Three dimensional perception: Understanding and appreciation of scale and proportions of objects, builing forms and elements, colour, texture, harmony and contrast. Design and drawing of geometrical or abstract shapes and patterns in pencil. Transformation of forms both 2D and 3D union, subtraction, rotation, development of surfaces and volumes. Generation of plans, elevations, and 3D views of objects. Creating 2-Dimensional and 3-Dimensional compositions using given shapes and forms.

## JEE Main Paper 2 (B.Planning) Drawing Syllabus

 Unit 1 General Awareness General Knowledge questions and knowledge about prominent cities, development issues, government programs etc. Unit 2 Social Sciences The idea about Nationalism, Nationalism in India, pre-modern world, 19th century global economy, colonialism and colonial cities, industrialization, resources and development, types of resources, agriculture, water, mineral resources, industries, national economy; Human settlements  Power-Sharing, federalism, political parties, democracy, the constitution of India Economic development-economic sectors, globalization, the concept of development, poverty; Population Structure, Social Exclusion, and inequality, urbanization, rural development, colonial cities Unit 3 Thinking Skills Comprehension (unseen passage); map reading skills, scale, distance, direction, area, etc; critical reasoning; understanding of charts, graphs and tables; basic concepts of statistics and quantitative reasoning

For updated information about JEE Main B.Arch (Paper 2) please visit www.jeemain.nic.in/

About the Author: Anu Handa is an Interior Designer, DIY Artist, Co-Founder and Educator at Mosaic Institute of Design. She has been the lead blogpost writer at www.mosaicdesigns.in since 2009. Her educational background in Interior Design, Urban Planning and the English Language has given her a broad base to cover a range of topics in her articles. Anu has spent 15+ years training Design & B.Arch Aspirants for entrance exams.

Passionate about Design Education, she’s briefly worked with Annamalai University as a paper setter for Design Exams. Likes to write about Design, Architecture and related fields, on online platforms like Quora. Aims at challenging the conventional & age old teaching methodology

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