# NDA Mathematics Syllabus 2021 – Get UPSC Maths Syllabus Here

**NDA stands for ( National Defence Academy )** it is the Premier Joint Training Institution and Center for Indian Army Force. And UPSC conducts the NDA examination.

In written exam and marking the answer, the candidates must use only black ball pen. Don’t use with any other colour pen. Candidates should now that there will be a negative marketing in the objective type question paper.

A candidate recommended by the Services Selection Board will undergo a medical examination by a Board of Service Medical Officers. Applicants will be informed of the time table and or examination place or candidates should note that no request for change of centre. In the online application form, the candidate should carefully choose the centre for the examination.

## Mathematics Subjects & Syllabus

## Mathematics:-

- Algebra
- Trigonometry
- Differential Calculus
- Matrices and Determination
- Analytical Geometry of two and three Dimensions
- Integral Calculus and Differential Equations
- Vector Algebra
- Statistics and Probability

## Algebra

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

Complex numbers—basic properties, modulus, and Binary system of numbers. Arithmetic, Geometric and Harmonic progressions. Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications.

## Trigonometry

Angles and their measures in degrees and radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae.

Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications – Height and distance, properties of triangles.

## Differential Calculus

Composite functions, one to one, onto and inverse functions. Derivative of function at a point, geometrical and physical interpretation of a derivative — applications.

Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.

## Matrices and Determination

Types of matrices, operations on matrices. The determinant of a matrix, basic properties of determinants.

Adjoin and the 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.

## Analytical Geometry of two and three Dimensions

Distance formula, Angle between two lines, Distance formula, Distance of a point from a line, Direction Cosines and direction ratios, Angle between two lines and an angle between two planes, the distance between two points, Standard forms of parabola, ellipse and hyperbola.

## Integral Calculus and Differential Equations

Evaluation of definite integrals—determination of areas of plane regions bounded by curves—applications. 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 differential equations, the solution of the first order and first-degree differential equations of various types—examples. Application in problems of growth and decay.

## Vector Algebra

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

## Statistics and Probability

**Statistics****:**

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

**Probability:**

Random variables function on a sample space. Binomial distribution, examples of random experiments giving rise to Binominal distribution. 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.

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