List of Most Important Topics for UPSC NDA (1) 2024 Mathematics & Preparation Tips

Name of the Exam

National Defence Academy Exam or NDA exam

Exam Conducting Body

Union Public Service Commission, UPSC

Frequency of NDA Exam

Two times a year (NDA 1 & NDA 2)

Selection Process

• Written Test 
• Intelligence & Personality Test (SSB)

Mode of exam

Offline (Pen and Paper mode)

Total Marks for NDA Maths

Total No. of Questions

Negative Marking

Exam Duration

Algebra

11

100

Trigonometry

05

50

Calculus

10

50

2D and 3D

08

10 to 15

Statistics and Probability

03

25

Chapter Name

Minimum average number of questions from each chapter

Algebra

(No. of Chapters: 11)

(No. of Important Chapters: 05)

Quadratic Equations

4

Complex Numbers

4

Matrices

4

Determinants

3

Permutations and Combinations

3

Trigonometry

(No. of Chapters: 05)

(No. of Important Chapters: 01)

Ratios and Identities

10

Calculus

(No. of Chapters: 10)

(No. of Important Chapters: 03)

Functions

6

Applications of Derivatives

6

Indefinite Integrals

3

2D and 3D

(No. of Chapters: 08)

(No. of Important Chapters: 02)

Straight Lines

5

3D

4

Statistics, Probability, and Binary Number

(No. of Chapters: 03)

(No. of Important Chapters: 02)

Statistics

8

Probability

8

Total No. of Chapters

37

Total No. of Important Chapters

13

Algebra

Sets, Venn Diagrams, De Morgan laws, Cartesian product, relation, equivalence relation. Real numbers, Complex numbers, Modulus, Cube roots, Conversion of a number in Binary system to Decimals and vice-versa, Arithmetic, Geometric and Harmonic Progressions, Quadratic equations, Linear inequations, Permutation and Combination, Binomial theorem and Logarithms, Binary System, Equivalence Relation, Cube root of unity, 2-D and 3-D Vectors, Magnitude and direction, Unit and null vectors, Vector Addition, Scalar multiplication of vectors, etc.

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, Continuity of functions, 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

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.

Integral Calculus and Differential Equation

• 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 differential equations, solution of first order and first-degree differential equations of various types—examples. Application in problems of growth and decay.
• Real valued function, Composite function, Range and graph of a function, Product and quotient of a function, Derivative of sum, Derivative of a function at a point, Derivative of function with respect to another function, Second order derivatives, Derivative of a composite function, Integration as inverse of differentiation, Increasing and decreasing functions, Integration by substitution and by parts, Trigonometric, exponential, and hyperbolic functions, Standard integrals, General and particular solution of a differential equation

Trigonometry

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

Vector Algebra

Vectors in two and three dimensions, magnitude, and direction of a vector. Unit and null vectors, the 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.

Analytical Geometry Of Two and Three Dimension

Rectangular Cartesian Coordinate system, Distance formula, Equation of a line in various forms. The angle between two lines. Distance of a point from a line. Equation of a circle in standard and in a general form. Standard forms of parabola, ellipse, and hyperbola. Eccentricity and axis of a conic. Point in a three-dimensional space, the 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.

Statistics and Probability

• 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 Binomial distribution.
• Frequency Distribution, Cumulative Frequency Distribution, Classification of data, Histogram, Pie Chart, Frequency Polygon, Variance and standard deviance, Random experiment, Outcomes and sample spaces, Correlation and regression, Events and types, Conditional probability, Measure of central tendency

Total No. of Questions

120

Correct Answer 

2.5 marks

Marks deducted for the wrong answer

- 0.83

Total duration of Mathematics Paper 

2 Hours 30 Minutes

Study Package Mathematics NDA/NA Entrance Exam

Arihant

Path Finder for NDA and NA National Defense Academy/Naval Academy Entrance Examination

Arihant

Mathematics for NDA and NA: National Defense Academy and Naval Academy

R S Aggarwal

Quantitative Aptitude for Competitive Examinations

R S Aggarwal

NDA Mathematics (Hindi)

RPH Editorial Board

NDA and NA Entrance Examination: Previous Solved Papers

R. Gupta

Mathematics Textbook for Class XI & XII

NCERT