## IAS Examination Syllabus : Mathematics

1. Algebra: Elements of Set Theory; Algebra of Real and Complex numbers including Demovire’s theorem; Polynomials and Polynomial equations, relation between Coefficients and Roots, symmetric functions of roots; Elements of Group Theory; Sub-Group, Cyclic groups, Permutation, Groups and their elementary properties. Rings, Integral Domains and Fields and their elementary properties.

2. Vector Spaces and Matrices: Vector Space, Linear Dependence and Independence. Sub-spaces. Basis and Dimensions, Finite Dimensional Vector Spaces. Linear Transformation of a Finite Dimensional Vector Space, Matrix Representation. Singular and Nonsingular Transformations. Rank and Nullity. Matrices : Addition, Multiplication, Determinants of a Matrix, Properties of Determinants of order, Inverse of a Matrix, Cramer’s rule.

3. Geometry and Vectors: Analytic Geometry of straight lines and conics in Cartesian and Polar coordinates; Three Dimensional geometry for planes, straight lines, sphere, cone and cylinder. Addition, Subtraction and Products of Vectors and Simple applications to Geometry.

4. Calculus: Functions, Sequences, Series, Limits, Continuity, Derivatives. Application of Derivatives : Rates of change, Tangents, Normals, Maxima, Minima, Rolle’s Theorem, Mean Value Theorems of Lagrange and Cauchy, Asymptotes, Curvature. Methods of finding indefinite integrals, Definite Integrals, Fundamental Theorem of integrals Calculus. Application of definite integrals to area, Length of a plane curve, Volume and Surfaces of revolution.

5. Ordinary Differential Equations: Order and Degree of a Differential Equation, First order differential Equations, Singular solution, Geometrical interpretation, Second order equations with constant coefficients.

6. Mechanics: Concepts of particles-Lamina; Rigid Body; Displacements; force; Mass; weight; Motion; Velocity; Speed; Acceleration; Parallelogram of forces; Parallelogram of velocity, acceleration; resultant; equilibrium of coplanar forces; Moments; Couples; Friction; Centre of mass, Gravity; Laws of motion; Motion of a particle in a straight line; simple Harmonic Motion; Motion under conservative forces; Motion under gravity; Projectile; Escape velocity; Motion of artificial satellites.

7. Elements of Computer Programming: Binary system, Octal and Hexadecimal systems. Conversion to and from Decimal systems. Codes, Bits, Bytes and Words. Memory of a computer, Arithmetic and Logical operations on numbers. Precisions. AND, OR, XOR, NOT and Shit/Rotate operators, Algorithms and Flow Charts.

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Regards

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For Detailed Information About IAS Examination

CLICK HERESIR I AM BTECH FINAL YEAR STUDENT AND MY BRACH IS ELECTRONICS AND INSTRUMENTATION I WANT TO KNOW ABOUT IAS EXAM SYLLABUS FOR PREPARATION WHAT SUBJECTS ARE REQUIRED IN IAS SIR PLS REPLY ME ON MY EMAIN ID

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i am the student of B.SC(MATH).i want to know about prepration of I.A.S examination

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sir ,i am the student of b.tech in me.i want to prepare for ias exam from now .i see the syllabus of mathematics and g.k but lam confused from where i firdt start to study and suggest me agood book of maths and g.k..please solve my problem,plese sir i am very confused

sir..i’m a b.tech c.s.e 3rd year student…could u tell me plz..which subjects should i choose ..for IAS exam…..