UPSC NDA 2021 Exam: Check Important Mathematics Topics (300 Marks) for Written NDA Exam

UPSC NDA 2021 Exam Important Mathematics Topics (300 Marks): Get the details of Important Topics for Mathematics Section of UPSC NDA & NA 2021 Written Exam which consists of 120 questions of 300 Marks .

UPSC NDA 2021 Exam: Check Important Mathematics Topics (300 Marks) for Written NDA Exam
UPSC NDA 2021 Exam: Check Important Mathematics Topics (300 Marks) for Written NDA Exam

UPSC NDA 2021 Exam Important Mathematics Topics (300 Marks): UPSC NDA 2021 Exam will be conducted on 18th April 2021. The Written Exam will consist of two papers, i.e., Mathematics (Paper-1) and General Ability Test (Paper-2). The written exam will be conducted for the recruitment in the Indian Army, Navy and Air Force wings of the National Defence Academy (NDA) and Naval Academy (NA). The latest exam pattern for UPSC NDA 2021 Exam Written Exam is as given below in the table:

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Subject/ No. of Questions



Maximum Marks

Mathematics (120 Questions)


2 Hours & 30 Minutes


General Ability Test (150 Questions)

English + General Knowledge


2 Hours & 30 Minutes




Get latest Exam Pattern & Syllabus of UPSC NDA 2021 Exam

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Candidates are advised to revise important topics of all the above sections to score high marks in UPSC NDA 2021 Exam. So, let’s have a look at the Important Mathematics Topics of UPSC NDA 2021 Exam which consists of 120 Questions of 300 Marks.

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UPSC NDA 2021: Mathematics Important Topics

The Questions will be of objective type with multiple choices and are likely to include questions pertaining to:

UPSC NDA Paper-1: Mathematics Important Topics (300 Marks)




Concept of set, operations on sets, Venn diagrams, De Morgan laws, Cartesian product, relation, equivalence relation.

Representation of real numbers on a line. Complex numbers—basic properties, modulus, argument, cube roots of unity. Binary system of numbers. Conversion of a number in decimal system to binary system and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. Solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications.

Matrices and Determinants

Types of matrices, operations on matrices. Determinant of a matrix, basic properties of determinants. Adjoint and inverse of a square matrix, Applications-Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.

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Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications-Height and distance, properties of triangles.

Analytical Geometry Of Two and Three Dimensions

Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in a three dimensional space, distance between two points. Direction Cosines and direction ratios. Equation two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

Practice UPSC NDA 2021: General Ability Test Part A – English Mock Test

Differential Calculus

Concept of a real valued function–domain, range and graph of a function. Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits—examples. Continuity of functions - examples, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivative-application. Derivatives of sum, product and quotient of functions, derivative of a function with respect to another function, derivative of a composite function. Second order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima

Integral Calculus and Differential Equations

Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals—determination of areas of plane regions bounded by curves—applications.

Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equations, solution of first order and first degree differential equations of various types—examples. Application in problems of growth and decay.

Practice UPSC NDA 2021 General Ability Test Part-B GK & Current Affairs Mock Test

Vector Algebra

Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, addition of vectors, scalar multiplication of a vector, scalar product or dot product of two vectors. Vector product or cross product of two vectors. Applications—work done by a force and moment of a force and in geometrical problems.

Statistics and Probability

Statistics: Classification of data, Frequency distribution, cumulative frequency distribution - examples. Graphical representation - Histogram, Pie Chart, frequency polygon—examples. Measures of Central tendency—Mean, median and mode. Variance and standard deviation determination and comparison. Correlation and regression.

Probability: Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary and composite events. Definition of probability—classical and statistical—examples. Elementary theorems on probability—simple problems. Conditional probability, Bayes’ theorem—simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binominal distribution.

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Important Points to Remember for UPSC NDA 2021 Written Exam

  1. The papers in all the subjects will consist of objective type questions
  2. The question papers (test booklets) of mathematics and Part “B” of General Ability Test will be set bilingually in Hindi as well as English.
  3. Candidates should note that there will be Negative Marking ofOne third for wrong answers marked by a candidate in the Objective Type Question Papers.

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  1. In the question papers, wherever necessary, questions involving the metric system of Weights and Measures only will be set.
  2. Candidates must write the papers in their own hand. In no circumstances will they be allowed the help of a scribe to write answers for them.
  3. The Commission has discretion to fix qualifying marks in any or all the subjects at the examination.

Click here to know the detailed Eligibility Criteria for UPSC NDA 2021 Exam

  1. The candidates are not permitted to use calculator or Mathematical or logarithmic table for answering objective type papers.

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