NDA Maths Paper- Chapter wise questions weightage

NDA Mathematics Syllabus, Chapter wise Pattern and Analysis of previous years NDA maths Paper:

NDA Mathematics Syllabus: (Maximum Marks-300)


  • 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 in equations of two variables by graphs.
  • Permutation and Combination.
  • Binomial theorem and its applications.
  • Logarithms and their applications.


  • 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.


  • 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.


  • 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.


  • 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—applications.
  • 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.


  • 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.


  • 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 :

  • 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.

Chapter wise NDA Maths Paper Pattern and Analysis

In Paper-I, Mathematics total questions are 120 for 300 marks and duration of exam is 2-1/2 Hours.

Analysis of Mathematics, NDA Exam (I), 2015 question paper:

(i) Sets and Functions = 8 questions

(ii) Algebra = 31 Questions

Complex Numbers = 6

Binary Numbers = 2

Sequence and Series = 2

Quadratic and Linear Equations = 4

Permutations and Combinations = 1

Binomial Theorem = 1

Logarithms = —

Matrix = 6

Determinants = 2

Vector Algebra = 7

(iii) Trigonometric = 12 Questions

Measurement and Angles and Trigonometric Ratio = 6

Inverse Trigonometric Functions = 4

Heights and Distances = 2

Properties of Triangles = —

(iv) Coordinate Geometry = 24 Questions

Coordinate System and Straight Lines = 7

Circle = 7

Conic Section = 2

3 D Geometry = 8

(v) Calculus = 36 Questions

Limits, Continuity and Differentiability = 9

Differentiation = 4

Application of Derivatives = 2

Indefinite Integral = 6

Definite Integral = 5

Area under the Curve = 4

Differential Equations = 6

(vi) Statistics and Probability = 15 Questions

Statistics = 7

Probability = 8

(vii) Miscellaneous = 1 Question

Previous years NDA Maths Paper:

Here are direct links of previous years NDA maths Paper (posted at UPSC’s officials website www.upsc.gov.in) for easy downloading.

  1.  2016 Exam-II
  2.  2016 Exam-I
  3.  2015 Exam-II
  4.  2015 Exam-I
  5.  2014 Exam-II
  6.  2014 Exam-I

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