Comprehensive NATA 2023 Syllabus: Topics, Exam Pattern, and Preparation Tips

NATA 2023 Syllabus

Mathematics

• Algebra: Definitions of A. P. and G.P.; Summation of first n-terms of series ∑n, ∑n²,∑n3 ; Arithmetic/Geometric series, General term; A.M., G.M. and their relation; Infinite G.P. series and its sum.

• 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).

• Logarithms: Definition, General properties & Change of base.

• Coordinate Geometry: Distance formula, condition of collinearity of three points in a plane, section formula, Polar coordinates, area of a triangle, transformation from Cartesian to polar coordinates and vice versa, Equation of lines indifferent forms, Parallel transformation of axes, Slope of a line, concept of locus, elementary locus problems, Condition of perpendicularity and parallelism of two lines, angle between two lines, Distance between two parallel lines. Distance of a point from a line, Lines through the point of intersection of two lines, Condition that a general equation of second degree in x, y may represent a circle, Equation of tangent, Equation of a circle in terms of endpoints of a diameter, Equation of a circle with a given center and radius, normal and chord, Parametric equation of a circle, Intersection of a line with a circle, Equation of common chord of two intersecting circles.

• Trigonometry: Trigonometric functions, formulae involving multiple and sub multiple angles, addition and subtraction formulae, general solution of trigonometric equations, Properties of triangles, inverse trigonometric functions and their properties

• Theory of Calculus: Functions, limit, continuity, chain rule, derivative of implicit functions and functions defined parametrically, composition of two functions, derivative, Integration as a reverse process of differentiation, Integration by parts, Integration by substitution and partial fraction, inverse of a function,  indefinite integral of standard functions, Definite integral as a limit of a sum with equal subdivisions. Properties of definite integrals, Fundamental theorem of integral calculus and its applications, solution of homogeneous differential equations, Formation of ordinary differential equations, linear first order differential equations, separation of variables method.

• Dimensional Co-ordinate Geometry: Direction cosines and direction ratios, equation of a straight line, distance between two points and section formula, equation of a plane, distance of a point from a plane

• Permutation and Combination: Permutation of n different things taken r at a time (r ≤ n), Permutation of n things not all different, Combinations of n different things taken r at a time (r ≤ n),Basic properties, Permutation with repetitions (circular permutation excluded), Combination of n things not all different, Problems involving both permutations and combinations

• Application of Calculus: Conditions of tangency, Determination of monotonicity, Tangents and normal, maxima and minima, Geometric interpretation of definite integral as area, calculation of area bounded by elementary curves and Straight lines, Differential coefficient as a measure of rate, Motion in a straight line with constant acceleration, Area of the region included between two elementary curves
• Statistics and Probability: Mean, variance and standard deviation, frequency distribution, Measure of dispersion, Addition and multiplication rules of probability, conditional probability and Bayes’ Theorem, independence of events, repeated independent trails and Binomial distribution
• General aptitude:

• Sets and Relations: Idea of sets, subsets, power set, union, intersection and difference of sets, complement, De Morgan’s Laws, Relation and its properties, Equivalence relation — definition and elementary examples, Venn diagram, etc.
• Mathematical Reasoning: Statements, logical operations like and, or, if and only if, implies, implied by; Understanding of tautology, converse, contradiction and contrapositive
• Drawing:
  • Understanding the Important Visual Principles in a Composition (2D or 3D) –  Direction, Rhythm, Hierarchy, Balance.
  • Solve Geometrical Puzzles , Understanding geometry and Ability to Visualize Shape.
  • Different Terminologies to Test Color Scheme Awareness, Understanding Color Theory and Knowledge
  • Perception to Test Graphical Similarities &  Visual System Interpretation & Other Properties
  • Ability to Understand Spatial Relationship between Objects and Scenarios and  to Visualize Images
  • Cognitive Ability
  • Perception, Memory, Recognition, Attention etc.

NATA 2023 Preparation Tips

• The candidates are advised to complete the preparation of the entire syllabus prior to the examination without skipping any part. 
• Referring to relevant textbooks and proper study materials of the latest editions will be helpful. 
• Once the preparation is completed, previous question papers and mock tests must be solved for getting a clearer idea on the type of questions asked. 
• Short notes, especially on drawing techniques must be made during the preparation for final reference. 
• The candidates are advised to keep revising the topics of doubt frequently.