The Union Public Service Commission (UPSC) holds a competitive examination named **Combined Defence Services (CDS) Examination ** for admissions to Indian Military Academy (IMA), Indian Naval Academy (INA), Air Force Academy (AFA) and Officers Training Academy (OTA). This examination is held twice a year, generally in the month of February and August. Blank application forms and other particulars are published in Employment News, generally in the month of August and March.

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The CDS syllabus details is given below.

## UPSC CDS Syllabus

### English Syllabus

The question paper is designed to test your understanding of English and workmanlike use of words.

Questions in English are from Synonyms, Antonyms, Reading Comprehension, Para Jumbles, Error Spotting, Jumbled Sentences, Sentence Correction and Fill in the Blanks.

### General Knowledge Syllabus

General Knowledge including knowledge of current events and of such matters of everyday observation and experience in scientific aspects as may be expected of an educated person who has not made a special study of any scientific subject. The paper also includes questions on History of India and Geography of a nature.

### UPSC CDS Elementary Mathematics Syllabus

**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, relation between its roots and coefficients (Only real roots to be considered). Simultaneous linear equations in two unknowns-analytical and graphical solutions. Simultaneous linear equations 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 x, cosine x, Tangent x when 0^{ }< x < 90 degrees, Values of sin x, cos x and tan x, for x = 0, 30, 45, 60 and 90 degrees, 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.

### Intelligence and Personality Test

In addition to the interview the candidates will be put to Intelligence Tests both verbal and non-verbal, designed to assess their basic intelligence. They will also be put to Group Tests such as group discussions, group planning, outdoor group tasks, and asked to give brief lectures on specified subjects. All these tests are intended to judge the mental calibre of a candidate. In broad terms, this is really an assessment of not only his intellectual qualities but also his social traits and interests in current affairs.