# Syllabus for Paper-2 (B.Arch) 2021

## 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: MATHEMATICAL INDUCTIONS:**

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 of Binomial coefficients and

simple applications.

**UNIT 7: 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 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

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 9: INTEGRAL CALCULAS:**

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.

Evaluation of simple integrals of the type

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 in standard form.

**UNIT 10: 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

**UNIT 11: 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.

**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 12: 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 13: VECTOR ALGEBRA**

Vectors and scalars, the addition of vectors,

components of a vector in two dimensions

and three-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

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, Bernoulli trials and binomial

distribution.

**UNIT 15: TRIGONOMETRY**

Trigonometrical identities and equations,

trigonometrical functions, inverse

trigonometrical functions and their

properties, heights and distance.

**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. 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.