As known to all UPSC organizes CDS exam twice each year. And, both the exams have English, General Knowledge and Elementary Mathematics as subjects.
So, here is the complete syllabus and standard of the Combined Defence Services Exam.
CDS Examination Standard
The standard of the English and General Knowledge is of graduation level and the standard for the Elementary Mathematics is of matriculation or 10+2 level.
CDS Examination Syllabus
The complete syllabus for the CDS written exam is as follows.
Candidate’s understanding of good English and workmanlike use of words.
General knowledge including current affairs, matters of everyday observation, basic knowledge of scientific aspects, History of India and basic knowledge of Geography.
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.
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.
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.
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.
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.
Collection and tabulation of statistical data, Graphical representation frequency polygons, histograms, bar charts, pie charts etc. Measures of central tendency.