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MATHEMATICS (10 topics) Subject

Algebra (6 subtopics) Topic

Definitions of A. P. and G.P.

General term

Summation of first n-terms of series

Arithmetic/Geometric series

A.M., G.M. and their relation

Infinite G.P. series and its sum

Logarithms (3 subtopics) Topic

Definition

General properties

Change of base

Matrices (10 subtopics) Topic

Concepts of m x n, real matrices

Operations of addition, scalar multiplication and multiplication of matrices

Transpose of a matrix

Determinant of a square matrix

Properties of determinants (statement only)

Minor, cofactor and adjoint of a matrix

Nonsingular matrix

Inverse of a matrix

Finding the area of a triangle

Solutions of system of linear equations (not more than 3 variables)

Trigonometry (6 subtopics) Topic

Trigonometric functions

Addition and subtraction formulae

Formulae involving multiple and submultiple angles

General solution of trigonometric equations

Properties of triangles

Inverse trigonometric functions and their properties

Coordinate Geometry (21 subtopics) Topic

Distance formula

Section formula

Area of a triangle

Condition of collinearity of three points in a plane

Polar coordinates, transformation from Cartesian to polar coordinates and vice versa

Parallel transformation of axes

Concept of locus, elementary locus problems

Slope of a line

Equation of lines in different forms

Angle between two lines

Condition of perpendicularity and parallelism of two lines

Distance of a point from a line

Distance between two parallel lines

Lines through the point of intersection of two lines

Equation of a circle with a given centre and radius

Condition that a general equation of second degree in x, y may represent a circle

Equation of a circle in terms of endpoints of a diameter

Equation of tangent, normal and chord

Parametric equation of a circle

Intersection of a line with a circle

Equation of common chord of two intersecting circles

3-Dimensional Coordinate Geometry (5 subtopics) Topic

Direction cosines and direction ratios

Distance between two points and section formula

Equation of a straight line

Equation of a plane

Distance of a point from a plane

Theory of Calculus (13 subtopics) Topic

Functions, composition of two functions and inverse of a function

Limit, continuity, derivative

Chain rule, derivatives of implicit functions and functions defined parametrically

Integration as a reverse process of differentiation

Indefinite integral of standard functions

Integration by parts, substitution and partial fraction

Definite integral as a limit of a sum with equal subdivisions

Fundamental theorem of integral calculus and its applications

Properties of definite integrals

Formation of ordinary differential equations

Solution of homogeneous differential equations

Separation of variables method

Linear first-order differential equations

Application of Calculus (7 subtopics) Topic

Tangents and normals, conditions of tangency

Determination of monotonicity, maxima, and minima

Differential coefficient as a measure of rate

Motion in a straight line with constant acceleration

Geometric interpretation of definite integral as area

Calculation of area bounded by elementary curves and straight lines

Area of the region included between two elementary curves

Permutation and Combination (7 subtopics) Topic

Permutation of n different things taken r at a time

Permutation of n things not all different

Permutation with repetitions (circular permutation excluded)

Combinations of n different things taken r at a time

Combination of n things not all different

Basic properties

Problems involving both permutations and combinations

Statistics and Probability (6 subtopics) Topic

Measure of dispersion, mean, variance and standard deviation

Frequency distribution

Addition and multiplication rules of probability

Conditional probability and Bayes’ theorem

Independence of events

Repeated independent trials and binomial distribution

GENERAL_APTITUDE (3 topics) Subject

Sets and Relations (5 subtopics) Topic

The idea of sets, subsets, power set

Complement, union, intersection and difference of sets

Venn diagram, De Morgan's laws

Relation and its properties

Equivalence relation — definition and elementary examples

Mathematical Reasoning (2 subtopics) Topic

Statements, logical operations like and, or, if and only if, implies, implied by

Understanding of tautology, converse, contradiction, and contrapositive

Objects (6 subtopics) Topic

Texture related to architecture and the built environment

Interpretation of pictorial compositions

Visualizing three-dimensional objects from two-dimensional drawing

Visualizing different sides of 3D objects

Analytical reasoning, mental ability (visual, numerical and verbal)

General awareness of national/international architects and famous architectural creations

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