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.

If you have questions, please ask below

16 Comments

  1. Tapajyoti Pal says:

    I wanna know all about IAS examination,, the syllabus, elligibility, duration, government institute etc..
    please Sir, mail me the enough informations about IAS examination, to give the examination..
    thank you…

  2. imtiyaz ahmad says:

    i want IAS.give me tips.

  3. Debendra Muduli says:

    Hello sir,
    I wanna to know about IAS examination,the sylabus,elligibility,duration. I have done my Btech in computer science and engineering.i am elligible for IAS exam or not ..plz sir give me the reply…i shall be obliged.

  4. Narendra Bishnoi says:

    sir, i m an third year student and i m doing engineering in IT branch. Next year is my final year. I want to know the syllabus of IAS pre. i also wanna know that whether an final year appearing student is eligible for IAS. Please mail me the whole information of IAS xam. Do reply ….plz

  5. devi says:

    hello sir,i have interested in ias.but i dont know what are the courses in that.just now i saw.so i want to choose mathematics sir.iam studying b.tech cse.now 2nd year.i want to improve my mindset related to ias course so what am i to do from just now…plz tell me
    thanking u sir……….

  6. balaji says:

    hello sir have interestet in ias. but i dott know are the courses in that.just now i saw.so i want to choose mathematice sir .iam studying b.tech cse.now 1st year.i want to improve my mindset related to ias course so what am i to do from just now… plz tell me
    thanking u sir…….

  7. MADHURI SHETTY says:

    Hello sir,i am interested in doing ias,but i don know about the courses available,can you please forward the subjects.i have just given my 6th semester exam of B.B.M course and i am awaiting for results,please provide proper guidelines.

    Regards

  8. saurav sarma says:

    what is the syllabus for ias??

  9. sonal rakholiya says:

    hello sir,
    i have completed my b.a.m.s. now i am interested in IAS.so give me the whole information about IAS examination.

  10. SAKSHI SINGH says:

    SIR 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

  11. priti says:

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

  12. devesh kumar pandey says:

    hi,
    sir
    i m pursuing B.Tech (CSE) and now m in the second year and interested in IAS so plz give me whole information about IAS examination i want to take math and i m confused about the second subject . plz help me and provide me the syllabus of the each subject.

  13. sanjay singh says:

    Sir give me tips about IAs

  14. akshay says:

    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

  15. kirandeep kaur says:

    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…..

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