UPSC Maths Optional Coaching for IAS

UPSC Maths Optional Coaching for IAS/IFoS

Live Online/Offline Classes by : K. Venkanna

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Indian Administrative Service (IAS) – Mathematics

Director Message

After spending many years in the field of teaching to IAS aspirants, I have analyzed very minutely the pros and cons of the entire system and the strategy prerequisite for this coveted examination. The civil services examination, the crème de la crème of all exams, is known as the toughest and the longest examination of the world. Therefore it becomes very important to share my own viewpoints for the bright future of the aspiring candidates. I have observed that the kind of phobia in the mindset of students for mathematics optional.

I can broadly categorize all science students specially mathematics background students who are preparing for this exam into two main categories. First category is of those students who opt mathematics as their one of the optional in this prestigious examination and the second category is of those students who do not opt this subject. I don’t have to say much about the first category of students as they are self motivate aspirants and moreover they have penchant for this subject. In fact, they are passionate and devoted for this and they can’t give ever the second thought as it seems that mathematics is in their bones…. Read More>>

Venkanna Sir 675x

K. Venkanna

Director - IMS (Institute of Mathematical Sciences)


Regular Batch

Weekend Batch

Admission Open, Limited Seats, available on first come first serve basis.


Schedule for IAS/IFoS Classroom Programme & Test Series Programme – 2023

* To cater the needs of students, occasionally IMS is conducting special batches with one chapter programme (efficiently) from 8:00 am to 8:00 pm on Friday




7:00 am to 9:30 am

-will be announced-

-will be announced-

11:15 am to 1:45 pm



2:15 pm to 4:45 pm



Fast Track Batch

5:15 pm Onwards



Previous Years IAS Mathematics Question Papers



Download Link

IAS – Mathematics Optional

2022 Question Paper

IAS – Mathematics Optional

2021 Question Paper

IAS – Mathematics Optional

2020 Question Paper

IAS – Mathematics Optional

2019 Question Paper

UPSC Maths Optional Coaching for IAS 1

Download IMS Information Brochure

Eligibility Criteria for IAS

The candidate must hold a degree of any of the Universities incorporated by an Act of the Central or State Legislature in India or other educational institutions established by an Act of Parliament or declared to be deemed as a University Under Section-3 of the University Grants Commission Act, 1956, or possess an equivalent qualification.

NOTE I : Candidates who have appeared at an examination the passing of which would render them educationally qualified for the Commission’s examination but have not been informed of the results as also the candidates who intend to appear at such a qualifying examination will also be eligible for admission to the Preliminary Examination. All candidates who are declared qualified by the Commission for taking the Civil Services (Main) Examination will be required to produce proof of passing the requisite examination with their application for the Main Examination failing which such candidates will not be admitted to the Main Examination. The applications for the Main Examination will be called sometime in the month of August/September.

IAS Mains Mathematics Syllabus


Linear Algebra: Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; Linear transformations, rank and nullity, matrix of a linear transformation.
Algebra of Matrices; Row and column reduction, Echelon form, congruence’s and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues.

Calculus: Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem, Taylor’s theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; Functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange’s method of multipliers, Jacobian.

Riemann’s definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple integrals (evaluation techniques only); Areas, surface and volumes.


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