How to Prepare Mathematics for NDA?

NDA (National Defense Academy) is a national level entrance exam which is conducted by UPSC (Union Public Service Commission). NDA is an offline (Pen and paper) exam conducted twice a year for recruitment in the National Defense Academy and the Indian Naval Academy. Interested applicants can apply on the official website of NDA i.e. Before applying for NDA, candidate are advised to check the Eligibility Criteria.

Class XII qualification is the minimum academic eligibility criterion the candidate needs to fulfill in order to be considered eligible to sit for the exam. They candidate may have done class XII from any recognized educational Board of India.

See Also : NDA 2019 Exam Pattern and Syllabus

Candidates who are appearing for the NDA exam are advised to go through the NDA Exam Pattern before starting preparations. The NDA exam is held in two parts- Paper 1 and Paper 2. Paper 1 consists of Mathematics and Paper 2 consists of General Ability and English. Both papers carry a total of 900 marks. Candidates are required to attempt total 220 questions in 2 hours 30 minutes. Negative marking is also applicable.

Paper 1:

This paper is based on Mathematics. All the questions will be related to Mathematics. Which test the calculation method, problem solving ability and other skills of candidates. All the questions of mathematics will be based on class 11th and 12th syllabus.

The structure of paper 1 is as follow:

Topic Mathematics

  • Question Format MCQ (Multiple Choice Questions)
  • Number of questions 120
  • Marks for correct answer 2.5 Marks
  • Negative marking for every wrong answer -0.83 marks
  • Exam duration 2 hours 30 minutes (150 minutes)
  • Total Marks 300

Paper 2:

This paper is based on general ability and English language. The duration of the exam is 2 hour 30 min. Paper 2 carry total 150 questions, all the questions will be in MCQ form. The total marks of paper 2 is 600 which is divided into two parts General ability is 400 marks and English language is 200 marks.

The structure of paper 2 is as follow

Topic General Ability and English

  • Question Format MCQ (Multiple Choice Questions)
  • Number of questions 150
  • Marks for correct answer 4 Marks
  • Negative marking for every wrong answer -1.33
  • Exam duration 2 hours 30 minutes (150 minutes)
  • Total Marks 600

NDA Mathematics Analysis

Mathematics is a very important subject to qualify NDA. Paper 1 is totally based on mathematics. Mathematics is all about calculation and formulas. NDA mathematics paper include 120 questions of 300 marks. Through this paper, examiners test math skills of candidates in many ways like how fast and accurate they are in basic calculation and concept and basic use of formulas.

Mathematics –

  • Algebra + Vector Algebra=  Marks – 75,  Number of Question- 30
  • Trigonometry= Marks – 50, Number of Question- 20
  • Determinants and matrices =Marks –  25 ,  Number of Question- 10
  • Analytical Geometry= Marks –  50 ,  Number of Question- 20
  • Vector Algebra= Marks – 25,  Number of Question- 10
  • Statistics and Probability= Marks – 25,  Number of Question- 10
  • Differential calculus and Integral calculus= Marks – 50,  Number of Question- 20
  • Total = Marks – 300, Number of Question- 120

Now, candidates know about the NDA exam pattern and mathematics structure of NDA exam. Then next step is preparation, before start preparation, candidates can go through the detail syllabus. Below we are going to discuss the detail syllabus of NDA mathematics exam.

NDA Mathematics Syllabus

Candidates who are applying for NDA. Before start preparation, candidates should check the proper syllabus of mathematics for better preparation. NDA mathematics syllabus is based on 11th and 12th class. These are few important topics of mathematics syllabus Algebra, Trigonometry, Determinants and matrices and other. Algebra is carry highest weightage. Here are the proper syllabus of NDA mathematics syllabus.

NDA Mathematic Topics Sub Topics

Algebra Concept of a 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 in equations of two variables by graphs, Permutation and Combination, Binomial theorem and its application, Logarithms and their applications.


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

Matrices and Determinants

Matrices and Determinants, Operations on matrices, Determinant of a matrix, Basic properties of determinants, Adjoint and inverse of a square matrix, Applications.

Analytical Geometry

Analytical Geometry 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.

Vector Algebra

Vector Algebra Vectors in two and three dimensions, Magnitude and direction of a vector, Unit and null vectors addition of vectors, Scalar multiplication of vector.

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.

See Also : Full Syllabus Of NDA

Differential calculus and Integral calculus

Differential calculus and Integral calculus Integration as inverse of differentiation, Integration by substitution and by parts, Standard integrals involving algebraic expressions, Trigonometric, Exponential and hyperbolic functions, General and particular solution of a differential equation.

Before start preparation, Candidates should check detail syllabus of NDA mathematic paper for preparation well.

  • Applicants should refer NCRT books of 11th and 12th level
  • Candidates should divide their time schedule according to paper
  • Candidates should start their preparation as soon as they can

Applicants should take the help of coaching centers, because coaching center provide better study material, tricks to solve questions etc.

  • Candidates should more focused on the topics which is carry highest weightage
  • Applicants should refer last year question papers

NDA 2017 Preparation Books

Books is the very important part of preparation. So, this is very important to choose a good book of good author. Below is the list of few important books for NDA 2017 preparation.

  1. 11th and 12th Mathematics books NCERT
  2. Mathematics for NDA and NA: National Defense Academy and Naval Academy by R S Aggarwal R S Aggarwal
  3. Pathfinder for NDA & NA Experts Compilation
  4. Objective General Knowledge & Current Affairs level 1 Disha Experts
  5. Objective General Knowledge & Current Affairs level 2 Disha Experts

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