APPENDIX I - Syllabus for
NATA-2018
Subject
|
|
|
|
|
Questions
|
|
Marks
|
|
Mode of Exam
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Mathematics
&
|
|
|
Mathematics
|
|
|
20
|
|
|
40
|
|
|
MCQ (Online)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
|
General
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
General Aptitude
|
40
|
|
80
|
|
|
MCQ (Online)
|
|
|||||
|
Aptitude
|
|
|
|
|
|
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Drawing test
|
|
|
|
|
02
|
|
|
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 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, 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.
Comments