JEE Main 2022 Syllabus B.Arch

Syllabus for Paper 2A (B.Arch)

MATHEMATICS

UNIT 1: SETS, RELATIONS, AND
FUNCTIONS:
UNIT 5: MATHEMATICAL INDUCTIONS:
Sets and their representation: Union,
Principle of Mathematical Induction and its
intersection and complement of sets and their
simple applications.
algebraic properties; Power set; Relation,
Type of relations, equivalence relations, UNIT 6: BINOMIAL THEOREM AND ITS
functions; one-one, into and onto functions, SIMPLE APPLICATIONS:
the composition of functions.
Binomial theorem for a positive integral
UNIT 2: COMPLEX NUMBERS AND index, general term and middle term,
QUADRATIC EQUATIONS: properties of Binomial coefficients, and
simple applications.
Complex numbers as ordered pairs of reals,
Representation of complex numbers in the UNIT 7: SEQUENCE AND SERIES:
form a + ib and their representation in a
plane, Argand diagram, algebra of complex Arithmetic and Geometric progressions,
number, modulus and argument (or insertion of arithmetic, geometric means
amplitude) of a complex number, triangle between two given numbers, Relation
inequality, Quadratic equations in real and between A.M and G.M sum up to n terms of
complex number system and their solutions special series; Sn, Sn2, Sn3. Arithmetico-
Relations between roots and co-efficient, Geometric progression.
nature of roots, the formation of quadratic UNIT 8: LIMIT, CONTINUITY, AND
equations with given roots. DIFFERENTIABILITY:
Real–valued functions, algebra of functions,
UNIT 3: MATRICES AND DETERMINANTS:
polynomials, rational, trigonometric,
Matrices, algebra of matrices, type of logarithmic, and exponential functions,
matrices, determinants, and matrices of order inverse function. Graphs of simple functions.
two and three, properties of determinants, Limits, continuity, and differentiability.
evaluation of determinants, area of triangles Differentiation of the sum, difference,
using determinants, Adjoint, and evaluation product, and quotient of two functions.
of inverse of a square matrix using Differentiation of trigonometric, inverse
determinants and elementary trigonometric, logarithmic, exponential,
transformations, Test of consistency and composite and implicit functions; derivatives
solution of simultaneous linear equations in of order up to two, Rolle’s and Lagrange's
two or three variables using determinants and Mean value Theorems, Applications of
matrices. derivatives: Rate of change of quantities,
monotonic-Increasing and decreasing
UNIT4:PERMUTATIONS AND functions, Maxima and minima of functions
COMBINATIONS: of one variable, tangents and normal.
The fundamental principle of counting, UNIT 9: INTEGRAL CALCULAS:
permutation as an arrangement and
combination as section, Meaning of P (n,r) Integral as an anti-derivative, Fundamental
and C (n,r), simple applications. Integrals involving algebraic, trigonometric,

exponential, and logarithms functions. passing through the point of intersection of
Integrations by substitution, by parts, and by two lines.
partial functions. Integration using
Circle, conic sections
trigonometric identities.
A standard form of equations of a circle, the
Evaluation of simple integrals of the type
general form of the equation of a circle, its
𝑑𝑥 𝑑𝑥 𝑑𝑥 𝑑𝑥 radius and central, equation of a circle when
∫ 𝑥 2 +𝑎2 , ∫ , ∫ 𝑎2 − 𝑥2 , ∫ 2 2
√𝑥 2 ± 𝑎2 √𝑎 − 𝑥
the endpoints of a diameter are given, points
𝑑𝑥 𝑑𝑥 (𝑝𝑥+𝑞)𝑑𝑥
, ∫ 𝑎𝑥 2 +𝑏𝑥+𝑐 ,∫ , ∫ 𝑎𝑥 2 +𝑏𝑥+𝑐 , of intersection of a line and a circle with the
√𝑎𝑥 2 + 𝑏𝑥+𝑐
centre at the origin and condition for a line to
(𝑝𝑥+𝑞)𝑑𝑥
∫ √𝑎𝑥 2 + 𝑏𝑥+𝑐 ∫ √𝑎2 ± 𝑥 2 𝑑𝑥 , be tangent to a circle, equation of the
tangent, sections of conics, equations of
∫ √𝑥 2 − 𝑎2 𝑑𝑥
conic sections (parabola, ellipse, and
Integral as limit of a sum. The fundamental hyperbola) in standard forms, condition for
theorem of calculus, properties of definite Y = mx + c to be a tangent and point (s) of
integrals. Evaluation of definite integrals, tangency.
determining areas of the regions bounded by
UNIT12:THREE DIMENSIONAL GEOMETRY
simple curves in standard form.
Coordinates of a point in space, the distance
UNIT 10: DIFFRENTIAL EQUATIONS
between two points, section formula,
Ordinary differential equations, their order, directions ratios, direction cosines, the angle
and degree, the formation of differential between two intersecting lines. Skew lines,
equations, solution of differential equation the shortest distance between them, and its
by the method of separation of variables, equation. Equations of a line and a plane in
solution of a homogeneous and linear different forms, the intersection of a line and
differential equation of the type a plane, coplanar lines.
𝑑𝑦 UNIT 13: VECTOR ALGEBRA
𝑑𝑥
+ 𝑝(𝑥)𝑦 = 𝑞(𝑥)
Vectors and scalars, the addition of vectors,
UNIT11: CO-ORDINATE GEOMETRY
components of a vector in two dimensions
Cartesian system of rectangular coordinates and three-dimensional space, scalar and
10 in a plane, distance formula, sections vector products, scalar and vector triple
formula, locus, and its equation, translation product.
of axis, slop of a line, parallel and
UNIT 14: STATISTICS AND PROBABILITY
perpendicular lines, intercept of a line on the
co-ordinate axes. Measures of discretion; calculation of mean,
median, mode of grouped and ungrouped
Straight line
data calculation of standard deviation,
Various forms of equations of a line, variance and mean deviation for grouped and
intersection of lines, angles between two ungrouped data.
lines, conditions for concurrence of three
Probability: Probability of an event, addition
lines, the distance of a point form a line,
and multiplication theorems of probability,
equations of internal and external by sectors
Baye's theorem, probability distribution of a
of angles between two lines co-ordinate of
random variate, Bernoulli trials, and
the centroid, orthocentre, and circumcentre
binomial distribution.
of a triangle, equation of the family of lines

UNIT 15: TRIGONOMETRY To be conducted in a Drawing sheet.

Trigonometrical identities and equations, Note: Candidates are advised to bring
trigonometrical functions, inverse pencils. Own geometry box set, crasets and
trigonometrical functions, and their colour pencils, and crayons for the Drawing
properties, heights, and distance. Test.

UNIT 16: 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-envirounmentVisusalising 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, 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 plans,
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. Jungle. Gardens, trees. Plants,
etc.) and rural life.