**SYLLABUS for JEE (Main)-2022**

**Syllabus for Paper-1 (B.E./B.Tech.)- MATHEMATICS**

**MATHEMATICS**

**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 function

**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, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangleinequality, Quadratic equations in real 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 and three, properties of determinants, evaluation of determinants, area of triangles using determinants, Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variablesusing determinants and matrices.

**UNIT 4: SEQUENCE 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 5: LIMIT,
CONTINUITY AND **

**DIFFERENTIABILITY:**

Real – valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponentialfunctions, 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 upto two, Rolle’s and Lagrange's Mean value Theorems, Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normal.

**UNIT 6: DIFFRENTIAL
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 a homogeneous and linear differential
equation of the type

dy/dx+ 𝑝(𝑥)𝑦 = 𝑞(𝑥)

**UNIT 7: CO-ORDINATE
GEOMETRY **

Cartesian system of rectangular co-ordinates in a plane, distance formula, sections formula, locus and its equation, translation of axes, the slope of a line, parallel and perpendicular lines, interceptsof a line on the co-ordinate axis. Straight lineVarious forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, the distance of a point form a line, equations of internal and external by sectors of angles between two lines coordinate of the centroid, orthocentre and circumcentre 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 radius and 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 be tangent 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 tangent and point (s) of tangency.

**UNIT 8: THREE
DIMENSIONAL GEOMETRY**

Coordinates of a point in space, the distance between two points, section formula, directions ratios and direction cosines, the angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.

**UNIT 9: STATISTICS
AND PROBABILITY**

Measures of discretion; calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.Probability: Probability of an event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a random variate, Bernoullitrials and binomial distribution.

**UNIT 10: TRIGONOMETRY**

Trigonometrical identities and equations, trigonometrical functions, inversetrigonometrical functions and their properties, heights and distance.

**SYLLABUS FOR JEE (Main)-2022**

**Syllabus for Paper-2A (B.Arch)**

**Part –I MATHEMATICS**

**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, modulus and argument (or amplitude) of a complex number, triangle inequality, Quadratic equations in real 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 and three, properties of determinants, evaluation of determinants, area of triangles using determinants, Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

**UNIT 4: PERMUTATIONS
AND COMBINATIONS:**

The fundamental principle of counting, permutation as an arrangement and combination as section, Meaning of P (n,r) and C (n,r), simple applications.

**UNIT 5: 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 Mean value Theorems, Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normal.

**UNIT 6: INTEGRAL
CALCULAS:**

Integral as an anti-derivative, FundamentalIntegrals involving algebraic, trigonometric, exponential and logarithms functions. Integrations by substitution, by parts and by partial functions. Integration using trigonometric identities.Evaluation of simple integrals of the type

Integral as limit of a sum. The fundamental theorem of calculus, properties of definiteintegrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

**UNIT 7: DIFFRENTIAL 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 a homogeneous and linear differential equation of the type

+ 𝑝(𝑥)𝑦 = 𝑞(𝑥)

**UNIT8: CO-ORDINATE
GEOMETRY **

Cartesian system of rectangular co-ordinates 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 line**

Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, the distance of a point form a line, equations of internal and external by sectors of angles between two lines co-ordinate of the centroid, orthocentre and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines.

**UNIT 9: DIFFRENTIAL 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 a homogeneous and linear differential equation of the type

dy/dx + 𝑝(𝑥)𝑦 = 𝑞(𝑥)

**Circle, conic
sections**

A standard form of equations of a circle, the general form of the equation of a circle, its radius and 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 be tangent 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 tangent and point (s) of tangency.

**UNIT 10: MATHEMATICAL
REASONING**

Statement logical operations and, or, implies, implied by, if and only if, understanding of tautology, contradiction, converse and contrapositive.

** ****Part –II APTITUDE**

**UNIT - 1 Awareness of
persons. Buildings, Materials.**

Objects, Texture related to Architecture and Build-envirounment Visusalising three dimensional objects from two-dimensional drawings. Visualising. 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, building 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 Plan, elevations and 3D views of objects, Creating two dimensional and three-dimensional compositions using given shapes and forms.

**Part – III DRAWING**

Sketching of scenes and activities from memory of urbanscape (public space, market, festivals, street scenes, monuments, recreational spaces etc). landscape (riverfronts. Jungles. Gardens, trees. Plants etc.) and rural life.

To be conducted in a Drawing sheet.

**Note**: Candidates are
advised to bring pencils. Own geometry box set, crasets and colour pencils and
crayons for the Drawing Test.