# CDS Exam Syllabus

## Combined Defence Service Exam

UPSC conducts Combined Defence Service (CDS) twice in a year to select candidates and admit them in prestigious Defence Institutions.

The selected students join one of the Institutions below:

### CDS Syllabus

The syllabus of the exam comprises of three subjects - English, General Knowledge and Elementary Mathematics. A student must study the syllabus of the exam before starting preparation. It helps in focused approach towards exam and gives an edge in competition.

### Details of the CDS Syllabus

#### English

The question paper will be designed to test the candidates understanding of English and workmanlike use of words.

#### General Knowledge

General Knowledge including knowledge of current, matters of everyday observation and experience in their scientific aspects as may be expected of an educated person who has not made a special study of any scientific subject. The paper will also include questions on History of India and Geography which candidates should be able to answer without special study.

#### Elementary Mathematics

##### Arithmetic

Number System Natural numbers, Integers, Rational and Real numbers. Fundamental operations, addition, subtraction, multiplication, division, Square roots, Decimal fractions. Unitary method, time and distance, time and work, percentages, applications to simple and compound interest, profit and loss, ratio and proportion, variation.

Elementary Number Theory Division algorithm. Prime and composite numbers. Tests of divisibility by 2, 3, 4, 5, 9 and 11. Multiples and factors. Factorisation Theorem. H.C.F. and L.C.M. Euclidean algorithm. Logarithms to base 10, laws of logarithms, use of logarithmic tables.

##### Algebra

Basic Operations, simple factors, Remainder Theorem, H.C.F., L.C.M., Theory of polynomials, solutions of quadratic equations, the relation between its roots and coefficients (Only real roots to be considered). Simultaneous linear equations in two unknowns analytical and graphical solutions. Simultaneous linear inequations in two variables and their solutions. Practical problems leading to two simultaneous linear equations or inequations in two variables or quadratic equations in one variable & their solutions. Set language and set notation, Rational expressions and conditional identities, Laws of indices.

##### Trigonometry

Sine , cosine , Tangent when 0 90 Values of sin , cos and tan , for = 0 , 30 , 45 , 60 and 90

Simple trigonometric identities.

Use of trigonometric tables.

Simple cases of heights and distances.

##### Geometry

Lines and angles, Plane and plane figures, Theorems on (i) Properties of angles at a point, (ii) Parallel lines, (iii) Sides and angles of a triangle, (iv) Congruency of triangles, (v) Similar triangles, (vi) Concurrence of medians and altitudes, (vii) Properties of angles, sides and diagonals of a parallelogram, rectangle and square, (viii) Circles and its properties including tangents and normals, (ix) Loci.

##### Mensuration

Areas of squares, rectangles, parallelograms, triangle and circle. Areas of figures which can be split up into these figures (Field Book), Surface area and volume of cuboids, lateral surface and volume of right circular cones and cylinders, surface area and volume of spheres.

##### Statistics

Collection and tabulation of statistical data, Graphical representation frequency polygons, histograms, bar charts, pie charts etc. Measures of central tendency.

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