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NATA Mock Test
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MATHEMATICS
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Algebra
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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
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Definition
General properties
Change of base
Matrices
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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
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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
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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
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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
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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
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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
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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
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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
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Sets and Relations
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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
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Statements, logical operations like and, or, if and only if, implies, implied by
Understanding of tautology, converse, contradiction, and contrapositive
Objects
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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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