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

## NDA Mathematics Syllabus: (Maximum Marks-300)

### ALGEBRA:

- 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.

### 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.

### TRIGONOMETRY :

- 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.

### 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—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.

### 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.

### 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.

## 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.