NATA Syllabus 2025 (Released) - Complete PDFs for Mathematics, General Aptitude, Drawing Test

Units

Topics Covered

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 coordinate geometry

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

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. 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 & 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 & 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.

Subject

Syllabus

Chemistry

Some Basic Concepts of Chemistry; Structure of Atom; Classification of Elements and Periodicity in Properties

Chemical Bonding and Molecular; States of Matter: Gases and Liquids

Chemical Thermodynamics; Equilibrium; Redox Reactions; Hydrogen; s- Block Elements p -Block Elements

Organic Chemistry: Some basic Principles and Techniques; Hydrocarbons; Environmental Chemistry

Physics

Electrostatics- Electric charges and Fields; Electrostatic Potential and Clearance

Current Electricity; Magnetic Effects of Current and Magnetism; Moving Charges and magnetism; Magnetism and Matter

Electromagnetic Induction and Alternating currents- Electromagnetic Induction; Alternating Current

Optics- Ray optics and optical instruments, Wave Optics Dual nature of radiation and Matter

Atoms and Nuclei- Atoms, Nuclei

Electronic devices- Semiconductor Electronics, Materials, Devices and Simple circuits.

Units

Topics Covered

General

Objects, 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

Mathematical Reasoning

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

Sets & 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.

Unit

Syllabus

Drawing

Understanding the important visual principles in a composition (2D OR 3D) such as balance, rhythm, direction, hierarchy, etc. Understanding geometry and the ability to visualize shape and solve geometrical puzzles to test spatial intelligence; Understanding color theory and the various terminologies to test color scheme awareness and knowledge; Visual system interpretation and perception to test graphical similarities and other properties; Ability to understand spatial relationship between objects, and to visualize images and scenarios; Tests for cognitive ability: perception, attention, recognition, memory etc.”