Syllabus for NATA-2018

(Part-A)

Mathematics 20 Questions; Marks 40 MCQ (OMR based)

General Aptitude 40 Questions; Marks 80 MCQ (OMR
based)

Drawing test (Part-B) 02 Questions; Marks 80 Paper
and Pencil

**MATHEMATICS**

Algebra: Definitions of
A. P. and G.P.; General term; Summation of first n-terms of series ∑n, ∑n²,∑n3
;

Arithmetic/Geometric series, A.M., G.M. and their
relation; Infinite G.P. series and its sum.

Logarithms: Definition;
General properties; Change of base.

Matrices: Concepts of m x
n (m ≤ 3, n ≤ 3) 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 area of a
triangle. Solutions of system of linear equations. (Not more than 3 variables).

Trigonometry: 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: 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 center 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 Co-ordinate geometry:
Direction cosines and direction ratios, distance between two pointsand section
formula, equation of a straight line, equation of a plane, distance of a point
from a plane.

Theory of Calculus:
Functions, composition of two functions and inverse of a function, limit,
continuity, derivative, chain rule, derivative of implicit functions and
functions defined parametrically. Integration as a reverse process of
differentiation, indefinite integral of standard functions. Integration by
parts. Integration by 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: 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: Permutation
of n different things taken r at a time (r ≤ n). Permutation of n things not
all different. Permutation with repetitions (circular permutation excluded).
Combinations of n different things taken r at a time (r ≤ n). Combination of n
things not all different. Basic properties. Problems involving both
permutations and combinations.

Statistics and Probability: 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 trails and
Binomial distribution.

GENERAL APTITUDE

Objects, texture related to architecture and built
environment. Interpretation of pictorial compositions,Visualizing
three-dimensional objects from two-dimensional drawing. Visualizing different
sides of 3Dobjects. Analytical reasoning, mental ability (visual, numerical and
verbal), General awareness of national/international architects and famous
architectural creations.

Mathematical reasoning:
Statements, logical operations like and, or, if and only if, implies, implied
by.Understanding of tautology, converse, contradiction
and contrapositive.

Sets and Relations: 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.

DRAWING TEST

Understanding of scale and proportion of objects,
geometric composition, shape, building forms andelements, aesthetics, colour texture,
harmony and contrast. Conceptualization and Visualization throughstructuring
objects in memory. Drawing of patterns - both geometrical and abstract. Form
transformations in2D and 3D like union, subtraction, rotation, surfaces and
volumes. Generating plan, elevation and 3D viewsof objects. Creating 2D and 3D
compositions using given shape and forms. Perspective drawing, Sketching ofurbanscape
and landscape, Common day-to-day life objects like furniture, equipment etc.,
from memory.